scholarly journals Track Layouts of Graphs

2004 ◽  
Vol Vol. 6 no. 2 ◽  
Author(s):  
Vida Dujmović ◽  
Attila Pór ◽  
David R. Wood
Keyword(s):  
Planar Graphs ◽  
Three Dimensional ◽  
Outerplanar Graphs ◽  
Linear Orderings ◽  
International Audience ◽  
The Relationship ◽  
Proper Vertex ◽  
Geometric Thickness ◽  
Dimensional Graph ◽  
Colour Classes

International audience A \emph(k,t)-track layout of a graph G consists of a (proper) vertex t-colouring of G, a total order of each vertex colour class, and a (non-proper) edge k-colouring such that between each pair of colour classes no two monochromatic edges cross. This structure has recently arisen in the study of three-dimensional graph drawings. This paper presents the beginnings of a theory of track layouts. First we determine the maximum number of edges in a (k,t)-track layout, and show how to colour the edges given fixed linear orderings of the vertex colour classes. We then describe methods for the manipulation of track layouts. For example, we show how to decrease the number of edge colours in a track layout at the expense of increasing the number of tracks, and vice versa. We then study the relationship between track layouts and other models of graph layout, namely stack and queue layouts, and geometric thickness. One of our principle results is that the queue-number and track-number of a graph are tied, in the sense that one is bounded by a function of the other. As corollaries we prove that acyclic chromatic number is bounded by both queue-number and stack-number. Finally we consider track layouts of planar graphs. While it is an open problem whether planar graphs have bounded track-number, we prove bounds on the track-number of outerplanar graphs, and give the best known lower bound on the track-number of planar graphs.\

scholarly journals Strong Oriented Chromatic Number of Planar Graphs without Short Cycles

2008 ◽  
Vol Vol. 10 no. 1 ◽  
Author(s):  
Mickael Montassier ◽  
Pascal Ochem ◽  
Alexandre Pinlou
Keyword(s):  
Abelian Group ◽  
Chromatic Number ◽  
Planar Graphs ◽  
Oriented Graph ◽  
Minimal Order ◽  
Outerplanar Graphs ◽  
International Audience

International audience Let M be an additive abelian group. An M-strong-oriented coloring of an oriented graph G is a mapping f from V(G) to M such that f(u) <> j(v) whenever uv is an arc in G and f(v)−f(u) <> −(f(t)−f(z)) whenever uv and zt are two arcs in G. The strong oriented chromatic number of an oriented graph is the minimal order of a group M such that G has an M-strong-oriented coloring. This notion was introduced by Nesetril and Raspaud [Ann. Inst. Fourier, 49(3):1037-1056, 1999]. We prove that the strong oriented chromatic number of oriented planar graphs without cycles of lengths 4 to 12 (resp. 4 or 6) is at most 7 (resp. 19). Moreover, for all i ≥ 4, we construct outerplanar graphs without cycles of lengths 4 to i whose oriented chromatic number is 7.

scholarly journals On the k-restricted structure ratio in planar and outerplanar graphs

2008 ◽  
Vol Vol. 10 no. 3 (Graph and Algorithms) ◽  
Author(s):  
Gruia Călinescu ◽  
Cristina G. Fernandes
Keyword(s):  
Approximation Algorithms ◽  
Planar Graphs ◽  
Rates Of Convergence ◽  
Simple Graph ◽  
Maximum Weight ◽  
Outerplanar Graphs ◽  
Weighted Version ◽  
International Audience ◽  
Unweighted Case

Graphs and Algorithms International audience A planar k-restricted structure is a simple graph whose blocks are planar and each has at most k vertices. Planar k-restricted structures are used by approximation algorithms for Maximum Weight Planar Subgraph, which motivates this work. The planar k-restricted ratio is the infimum, over simple planar graphs H, of the ratio of the number of edges in a maximum k-restricted structure subgraph of H to the number edges of H. We prove that, as k tends to infinity, the planar k-restricted ratio tends to 1 = 2. The same result holds for the weighted version. Our results are based on analyzing the analogous ratios for outerplanar and weighted outerplanar graphs. Here both ratios tend to 1 as k goes to infinity, and we provide good estimates of the rates of convergence, showing that they differ in the weighted from the unweighted case.

scholarly journals Linear choosability of graphs

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Louis Esperet ◽  
Mickael Montassier ◽  
André Raspaud
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Oriented Graph ◽  
Vertex Coloring ◽  
Proper Coloring ◽  
Maximum Average Degree ◽  
Complete Problem ◽  
International Audience ◽  
Np Complete ◽  
Proper Vertex

International audience A proper vertex coloring of a non oriented graph $G=(V,E)$ is linear if the graph induced by the vertices of two color classes is a forest of paths. A graph $G$ is $L$-list colorable if for a given list assignment $L=\{L(v): v∈V\}$, there exists a proper coloring $c$ of $G$ such that $c(v)∈L(v)$ for all $v∈V$. If $G$ is $L$-list colorable for every list assignment with $|L(v)|≥k$ for all $v∈V$, then $G$ is said $k$-choosable. A graph is said to be lineary $k$-choosable if the coloring obtained is linear. In this paper, we investigate the linear choosability of graphs for some families of graphs: graphs with small maximum degree, with given maximum average degree, planar graphs... Moreover, we prove that determining whether a bipartite subcubic planar graph is lineary 3-colorable is an NP-complete problem.

scholarly journals 8-star-choosability of a graph with maximum average degree less than 3

2011 ◽  
Vol Vol. 13 no. 3 (Graph and Algorithms) ◽  
Author(s):  
Min Chen ◽  
André Raspaud ◽  
Weifan Wang
Keyword(s):  
Graph Theory ◽  
Chromatic Number ◽  
Planar Graphs ◽  
Average Degree ◽  
Vertex Coloring ◽  
Maximum Average Degree ◽  
International Audience ◽  
Star Coloring ◽  
List Chromatic Number ◽  
Proper Vertex

Graphs and Algorithms International audience A proper vertex coloring of a graphGis called a star-coloring if there is no path on four vertices assigned to two colors. The graph G is L-star-colorable if for a given list assignment L there is a star-coloring c such that c(v) epsilon L(v). If G is L-star-colorable for any list assignment L with vertical bar L(v)vertical bar \textgreater= k for all v epsilon V(G), then G is called k-star-choosable. The star list chromatic number of G, denoted by X-s(l)(G), is the smallest integer k such that G is k-star-choosable. In this article, we prove that every graph G with maximum average degree less than 3 is 8-star-choosable. This extends a result that planar graphs of girth at least 6 are 8-star-choosable [A. Kundgen, C. Timmons, Star coloring planar graphs from small lists, J. Graph Theory, 63(4): 324-337, 2010].

Contractual Relationships among Artists, Record Labels, and Artist Management Companies in Japan

2020 ◽  
Author(s):  
Kazuhiro Ando
Keyword(s):  
Music Industry ◽  
Music Business ◽  
Know How ◽  
Contractual Relationships ◽  
The World ◽  
Employee Relationship ◽  
International Audience ◽  
Music Market ◽  
Japanese Music ◽  
The Relationship

Although Japan is the second largest music market in the world, the structure and practices of the music industry are little understood internationally. People overseas need to know how the music business works in Japan so that they can conduct business comfortably. The Japanese music industry has unique features in some respects. First, Japanese record labels remain heavily dependent on traditional physically packaged music although its profitability is much lower than that of digital distribution. Second, full-scale competition in the music copyright management business has just begun. While JASRAC monopolized this market for more than sixty years, the new entrant, NexTone has gradually increased the market share thanks to the frustration experienced by many music publishers and songwriters in their dealings with JASRAC. Third, the relationship between artists and artist management companies is more like an employer-employee relationship than a client-agent relationship. Artist management companies are fully invested in discovering, nurturing, and marketing young artists just the way big businesses handle their recruits. This chapter illuminates practices of the Japanese music industry for an international audience.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

scholarly journals Clustered 3-colouring graphs of bounded degree

2021 ◽  
pp. 1-13
Author(s):  
Vida Dujmović ◽  
Louis Esperet ◽  
Pat Morin ◽  
Bartosz Walczak ◽  
David R. Wood
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Bounded Degree ◽  
Bounded Number ◽  
Proper Vertex ◽  
Vertex Colouring

Abstract A (not necessarily proper) vertex colouring of a graph has clustering c if every monochromatic component has at most c vertices. We prove that planar graphs with maximum degree $\Delta$ are 3-colourable with clustering $O(\Delta^2)$ . The previous best bound was $O(\Delta^{37})$ . This result for planar graphs generalises to graphs that can be drawn on a surface of bounded Euler genus with a bounded number of crossings per edge. We then prove that graphs with maximum degree $\Delta$ that exclude a fixed minor are 3-colourable with clustering $O(\Delta^5)$ . The best previous bound for this result was exponential in $\Delta$ .

scholarly journals A Field Measurement Based Wind Characteristics Analysis of a Typhoon in Near-Ground Boundary Layer

Atmosphere ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 873
Author(s):  
Dandan Xia ◽  
Liming Dai ◽  
Li Lin ◽  
Huaifeng Wang ◽  
Haitao Hu
Keyword(s):  
Turbulence Intensity ◽  
Field Measurement ◽  
Three Dimensional ◽  
Wind Data ◽  
Statistical Characteristics ◽  
Gust Factor ◽  
Characteristics Analysis ◽  
Wind Characteristics ◽  
The Mean ◽  
The Relationship

The field measurement was conducted to observe the wind field data of West Pacific typhoon “Maria” in this research. With the application of ultrasonic anemometers installed in different heights (10 m, 80 m, 100 m) of the tower, the three dimensional wind speed data of typhoon “Maria” was acquired. In addition, vane-type anemometers were installed to validate the accuracy of the wind data from ultrasonic anemometers. Wind characteristics such as the mean wind profile, turbulence intensity, integral length scale, and wind spectrum are studied in detail using the collected wind data. The relationship between the gust factor and turbulence intensity was also studied and compared with the existing literature to demonstrate the characteristics of Maria. The statistical characteristics of the turbulence intensity and gust factor are presented. The corresponding conclusion remarks are expected to provide a useful reference for designing wind-resistant buildings and structures.

scholarly journals Three-dimensional relationships between tumor cells and microcirculation with double cyanine immunolabeling, laser scanning confocal microscopy, and computer-assisted reconstruction: an alternative to cast corrosion preparations.

1994 ◽  
Vol 42 (5) ◽  
pp. 681-686 ◽  
Author(s):  
V Rummelt ◽  
L M Gardner ◽  
R Folberg ◽  
S Beck ◽  
B Knosp ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Blood Vessels ◽  
Tumor Cells ◽  
Laser Scanning ◽  
Three Dimensional ◽  
Melanoma Cells ◽  
Tumor Blood Vessels ◽  
The Relationship ◽  
Scanning Electron

The morphology of the microcirculation of uveal melanomas is a reliable market of tumor progression. Scanning electron microscopy of cast corrosion preparations can generate three-dimensional views of these vascular patterns, but this technique sacrifices the tumor parenchyma. Formalin-fixed wet tissue sections 100-150 microns thick from uveal melanomas were stained with the lectin Ulex europaeus agglutinin I (UEAI) and proliferating cell nuclear antigen (PCNA) to demonstrate simultaneously the tumor blood vessels and proliferating tumor cells. Indocarbocyanine (Cy3) was used as a fluorophore for UEAI and indodicarbocyanine (Cy5) was used for PCNA. Double labeled sections were examined with a laser scanning confocal microscope. Images of both stains were digitized at the same 5-microns intervals and each of the two images per interval was combined digitally to form one image. These combined images were visualized through voxel processing to study the relationship between melanoma cells expressing PCNA and various microcirculatory patterns. This technique produces images comparable to scanning electron microscopy of cast corrosion preparations while permitting simultaneous localization of melanoma cells expressing PCNA. The microcirculatory tree can be viewed from any perspective and the relationship between tumor cells and the tumor blood vessels can be studied concurrently in three dimensions. This technique is an alternative to cast corrosion preparations.

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