scholarly journals Algorithms for Outerplanar Graph Roots and Graph Roots of Pathwidth at Most 2

2017 ◽  
pp. 275-288 ◽  
Author(s):  
Petr A. Golovach ◽  
Pinar Heggernes ◽  
Dieter Kratsch ◽  
Paloma T. Lima ◽  
Daniël Paulusma
Keyword(s):  
Outerplanar Graph

scholarly journals On edge-intersection graphs of k-bend paths in grids

2010 ◽  
Vol Vol. 12 no. 1 ◽  
Author(s):  
Therese Biedl ◽  
Michal Stern
Keyword(s):  
Conflict Resolution ◽  
Planar Graph ◽  
Bipartite Graph ◽  
Outerplanar Graph ◽  
Line Graphs ◽  
Intersection Graphs ◽  
Grid Networks ◽  
Graph Classes ◽  
International Audience ◽  
Number Of Bends

International audience Edge-intersection graphs of paths in grids are graphs that can be represented such that vertices are paths in a grid and edges between vertices of the graph exist whenever two grid paths share a grid edge. This type of graphs is motivated by applications in conflict resolution of paths in grid networks. In this paper, we continue the study of edge-intersection graphs of paths in a grid, which was initiated by Golumbic, Lipshteyn and Stern. We show that for any k, if the number of bends in each path is restricted to be at most k, then not all graphs can be represented. Then we study some graph classes that can be represented with k-bend paths, for small k. We show that every planar graph has a representation with 5-bend paths, every outerplanar graph has a representation with 3-bend paths, and every planar bipartite graph has a representation with 2-bend paths. We also study line graphs, graphs of bounded pathwidth, and graphs with -regular edge orientations.

Learning Block-Preserving Outerplanar Graph Patterns and Its Application to Data Mining

2008 ◽  
pp. 330-347 ◽  
Author(s):  
Hitoshi Yamasaki ◽  
Yosuke Sasaki ◽  
Takayoshi Shoudai ◽  
Tomoyuki Uchida ◽  
Yusuke Suzuki
Keyword(s):  
Data Mining ◽  
Outerplanar Graph

scholarly journals Some New Classes of Open Distance-Pattern Uniform Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Bibin K. Jose
Keyword(s):  
Nonempty Subset ◽  
Chordal Graphs ◽  
Outerplanar Graph ◽  
Outerplanar Graphs ◽  
Induced Subgraphs ◽  
Minimum Cardinality ◽  
Maximal Outerplanar Graphs ◽  
Split Graphs ◽  
Strongly Chordal Graphs

Given an arbitrary nonempty subset M of vertices in a graph G=(V,E), each vertex u in G is associated with the set fMo(u)={d(u,v):v∈M,u≠v} and called its open M-distance-pattern. The graph G is called open distance-pattern uniform (odpu-) graph if there exists a subset M of V(G) such that fMo(u)=fMo(v) for all u,v∈V(G), and M is called an open distance-pattern uniform (odpu-) set of G. The minimum cardinality of an odpu-set in G, if it exists, is called the odpu-number of G and is denoted by od(G). Given some property P, we establish characterization of odpu-graph with property P. In this paper, we characterize odpu-chordal graphs, and thereby characterize interval graphs, split graphs, strongly chordal graphs, maximal outerplanar graphs, and ptolemaic graphs that are odpu-graphs. We also characterize odpu-self-complementary graphs, odpu-distance-hereditary graphs, and odpu-cographs. We prove that the odpu-number of cographs is even and establish that any graph G can be embedded into a self-complementary odpu-graph H, such that G and G¯ are induced subgraphs of H. We also prove that the odpu-number of a maximal outerplanar graph is either 2 or 5.

scholarly journals The surviving rate of an outerplanar graph for the firefighter problem

2011 ◽  
Vol 412 (8-10) ◽  
pp. 913-921 ◽  
Author(s):  
Weifan Wang ◽  
Xubin Yue ◽  
Xuding Zhu
Keyword(s):  
Outerplanar Graph ◽  
Surviving Rate ◽  
Firefighter Problem

scholarly journals The Tutte Polynomial Characterizes Simple Outerplanar Graphs

2011 ◽  
Vol 20 (4) ◽  
pp. 609-616 ◽  
Author(s):  
A. J. GOODALL ◽  
A. de MIER ◽  
S. D. NOBLE ◽  
M. NOY
Keyword(s):  
Tutte Polynomial ◽  
Outerplanar Graph ◽  
Outerplanar Graphs

We show that if G is a simple outerplanar graph and H is a graph with the same Tutte polynomial as G, then H is also outerplanar. Examples show that the condition of G being simple cannot be omitted.

Study on Electronic Industry with an Application of Rectilinear Embedding in VLSI Placement

2013 ◽  
Vol 345 ◽  
pp. 355-358
Author(s):  
Li Yan Pan ◽  
Yan Pei Liu
Keyword(s):  
Large Scale ◽  
Outerplanar Graph ◽  
Electronic Industry ◽  
Lagrangian Inversion ◽  
Multiple Parameters ◽  
Vlsi Physical Design ◽  
Wide Range ◽  
Large Scale Integration ◽  
Scale Integration ◽  
The Relationship

The electronic industry has developed quickly in last few years, with the rapid growth of Very Large Scale Integration technology. Placement layout is considered as the original step in VLSI physical design. The rectilinear embedding, which originates from graph theory, has wide range of application in VLSI placement. In this paper, we constructed a mathematical model for VLSI placement. Firstly, the VLSI placement was converted to quadrangulation by using rectilinear embedding speculative knowledge. Then we provided generating functions for two types of quadrangulations with graph multiple parameters. And the explicit formulae were obtained by employing Lagrangian inversion. Furthermore, we found the relationship between outerplanar graph and Hamilton graph, so the counting result of Hamilton quadrangulation was derived. The quadrangulation calculation can be applied to the establishment of arithmetical algorithms, which can be widely used in the optimization of VLSI placement.

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