scholarly journals Immersion containment and connectivity in color-critical graphs

2012 ◽  
Vol Vol. 14 no. 2 (Graph Theory) ◽  
Author(s):  
Faisal N. Abu-Khzam ◽  
Michael A. Langston
Keyword(s):  
Graph Theory ◽  
Graph Coloring ◽  
Supporting Evidence ◽  
Vertex Connectivity ◽  
Edge Connectivity ◽  
Critical Graphs ◽  
International Audience ◽  
The Relationship

Graph Theory International audience The relationship between graph coloring and the immersion order is considered. Vertex connectivity, edge connectivity and related issues are explored. It is shown that a t-chromatic graph G contains either an immersed Kt or an immersed t-chromatic subgraph that is both 4-vertex-connected and t-edge-connected. This gives supporting evidence of our conjecture that if G requires at least t colors, then Kt is immersed in G.

scholarly journals Connectivity in Hypergraphs

2018 ◽  
Vol 61 (2) ◽  
pp. 252-271 ◽  
Author(s):  
Megan Dewar ◽  
David Pike ◽  
John Proos
Keyword(s):  
Polynomial Time ◽  
The Other ◽  
Np Hard ◽  
Vertex Connectivity ◽  
Edge Connectivity ◽  
The Relationship ◽  
Weak Edge ◽  
Edge Size

AbstractIn this paper we consider two natural notions of connectivity for hypergraphs: weak and strong. We prove that the strong vertex connectivity of a connected hypergraph is bounded by its weak edge connectivity, thereby extending a theorem of Whitney from graphs to hypergraphs. We find that, while determining a minimum weak vertex cut can be done in polynomial time and is equivalent to finding a minimum vertex cut in the 2-section of the hypergraph in question, determining a minimum strong vertex cut is NP-hard for general hypergraphs. Moreover, the problem of finding minimum strong vertex cuts remains NP-hard when restricted to hypergraphs with maximum edge size at most 3. We also discuss the relationship between strong vertex connectivity and the minimum transversal problem for hypergraphs, showing that there are classes of hypergraphs for which one of the problems is NP-hard, while the other can be solved in polynomial time.

scholarly journals The generalized 3-connectivity of Cartesian product graphs

2012 ◽  
Vol Vol. 14 no. 1 (Graph Theory) ◽  
Author(s):  
Hengzhe Li ◽  
Xueliang Li ◽  
Yuefang Sun
Keyword(s):  
Graph Theory ◽  
Positive Integer ◽  
Cartesian Product ◽  
Vertex Connectivity ◽  
Connected Graphs ◽  
Generalized Connectivity ◽  
Product Graphs ◽  
International Audience ◽  
Cartesian Product Graphs ◽  
Internally Disjoint Trees

Graph Theory International audience The generalized connectivity of a graph, which was introduced by Chartrand et al. in 1984, is a generalization of the concept of vertex connectivity. Let S be a nonempty set of vertices of G, a collection \T-1, T (2), ... , T-r\ of trees in G is said to be internally disjoint trees connecting S if E(T-i) boolean AND E(T-j) - empty set and V (T-i) boolean AND V(T-j) = S for any pair of distinct integers i, j, where 1 <= i, j <= r. For an integer k with 2 <= k <= n, the k-connectivity kappa(k) (G) of G is the greatest positive integer r for which G contains at least r internally disjoint trees connecting S for any set S of k vertices of G. Obviously, kappa(2)(G) = kappa(G) is the connectivity of G. Sabidussi's Theorem showed that kappa(G square H) >= kappa(G) + kappa(H) for any two connected graphs G and H. In this paper, we prove that for any two connected graphs G and H with kappa(3) (G) >= kappa(3) (H), if kappa(G) > kappa(3) (G), then kappa(3) (G square H) >= kappa(3) (G) + kappa(3) (H); if kappa(G) = kappa(3)(G), then kappa(3)(G square H) >= kappa(3)(G) + kappa(3) (H) - 1. Our result could be seen as an extension of Sabidussi's Theorem. Moreover, all the bounds are sharp.

scholarly journals The generalized 3-connectivity of Lexicographic product graphs

2014 ◽  
Vol Vol. 16 no. 1 (Graph Theory) ◽  
Author(s):  
Xueliang Li ◽  
Yaping Mao
Keyword(s):  
Graph Theory ◽  
Cartesian Product ◽  
Natural Generalization ◽  
Upper Bounds ◽  
Lexicographic Product ◽  
Vertex Connectivity ◽  
Connected Graphs ◽  
Product Graphs ◽  
International Audience ◽  
Lexicographic Product Graphs

Graph Theory International audience The generalized k-connectivity κk(G) of a graph G, first introduced by Hager, is a natural generalization of the concept of (vertex-)connectivity. Denote by G^H and G&Box;H the lexicographic product and Cartesian product of two graphs G and H, respectively. In this paper, we prove that for any two connected graphs G and H, κ3(G^H)&#x2265; κ3(G)|V(H)|. We also give upper bounds for κ3(G&Box; H) and κ3(G^H). Moreover, all the bounds are sharp.

scholarly journals Symmetric bipartite graphs and graphs with loops

2015 ◽  
Vol Vol. 17 no. 1 (Graph Theory) ◽  
Author(s):  
Grant Cairns ◽  
Stacey Mendan
Keyword(s):  
Graph Theory ◽  
Bipartite Graph ◽  
Degree Sequence ◽  
Bipartite Graphs ◽  
Degree Sequences ◽  
Graph Automorphism ◽  
International Audience ◽  
The Relationship

Graph Theory International audience We show that if the two parts of a finite bipartite graph have the same degree sequence, then there is a bipartite graph, with the same degree sequences, which is symmetric, in that it has an involutive graph automorphism that interchanges its two parts. To prove this, we study the relationship between symmetric bipartite graphs and graphs with loops.

scholarly journals Connectivity of Fibonacci cubes, Lucas cubes and generalized cubes

2015 ◽  
Vol Vol. 17 no. 1 (Graph Theory) ◽  
Author(s):  
Jernej Azarija ◽  
Sandi Klavžar ◽  
Jaehun Lee ◽  
Yoomi Rho
Keyword(s):  
Graph Theory ◽  
Positive Integer ◽  
Minimum Degree ◽  
Edge Connectivity ◽  
Binary Word ◽  
Fibonacci Cube ◽  
International Audience ◽  
Lucas Cube

Graph Theory International audience If f is a binary word and d a positive integer, then the generalized Fibonacci cube Qd(f) is the graph obtained from the d-cube Qd by removing all the vertices that contain f as a factor, while the generalized Lucas cube Qd(lucas(f)) is the graph obtained from Qd by removing all the vertices that have a circulation containing f as a factor. The Fibonacci cube Γd and the Lucas cube Λd are the graphs Qd(11) and Qd(lucas(11)), respectively. It is proved that the connectivity and the edge-connectivity of Γd as well as of Λd are equal to ⌊ d+2 / 3⌋. Connected generalized Lucas cubes are characterized and generalized Fibonacci cubes are proved to be 2-connected. It is asked whether the connectivity equals minimum degree also for all generalized Fibonacci/Lucas cubes. It was checked by computer that the answer is positive for all f and all d≤9.

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 p-box: a new graph model

2015 ◽  
Vol Vol. 17 no. 1 (Graph Theory) ◽  
Author(s):  
Mauricio Soto ◽  
Christopher Thraves-Caro
Keyword(s):  
Graph Theory ◽  
Graph Model ◽  
Directed Path ◽  
Outerplanar Graphs ◽  
New Model ◽  
Model Based ◽  
Representative Element ◽  
International Audience ◽  
Graph Families

Graph Theory International audience In this document, we study the scope of the following graph model: each vertex is assigned to a box in ℝd and to a representative element that belongs to that box. Two vertices are connected by an edge if and only if its respective boxes contain the opposite representative element. We focus our study on the case where boxes (and therefore representative elements) associated to vertices are spread in ℝ. We give both, a combinatorial and an intersection characterization of the model. Based on these characterizations, we determine graph families that contain the model (e. g., boxicity 2 graphs) and others that the new model contains (e. g., rooted directed path). We also study the particular case where each representative element is the center of its respective box. In this particular case, we provide constructive representations for interval, block and outerplanar graphs. Finally, we show that the general and the particular model are not equivalent by constructing a graph family that separates the two cases.

scholarly journals Graphs with many vertex-disjoint cycles

2012 ◽  
Vol Vol. 14 no. 2 (Graph Theory) ◽  
Author(s):  
Dieter Rautenbach ◽  
Friedrich Regen
Keyword(s):  
Graph Theory ◽  
Upper Bound ◽  
Linear Time ◽  
Simple Extension ◽  
Disjoint Cycles ◽  
Cyclomatic Number ◽  
Finite Set ◽  
Extension Rule ◽  
International Audience ◽  
Vertex Disjoint

Graph Theory International audience We study graphs G in which the maximum number of vertex-disjoint cycles nu(G) is close to the cyclomatic number mu(G), which is a natural upper bound for nu(G). Our main result is the existence of a finite set P(k) of graphs for all k is an element of N-0 such that every 2-connected graph G with mu(G)-nu(G) = k arises by applying a simple extension rule to a graph in P(k). As an algorithmic consequence we describe algorithms calculating minmu(G)-nu(G), k + 1 in linear time for fixed k.

Eucalyptus Physiology. III. Frost Resistance.

1981 ◽  
Vol 29 (6) ◽  
pp. 675 ◽  
Author(s):  
DM Paton
Keyword(s):  
Frost Resistance ◽  
Eucalyptus Species ◽  
Supporting Evidence ◽  
Light Conditions ◽  
Root Temperature ◽  
Resistant Species ◽  
Electron Transport Properties ◽  
Active Electron ◽  
The Relationship

The effects of different hardening regimes were studied in E. viminalis by varying temperature, light conditions and photoperiod. The role of root temperature in dehardening was investigated in E. grandis. The relationship between leaf glaucousness and frost resistance was reexamined in E. urnigera and in crosses between the glaucous frost-resistant species E. pulverulenta and the green. less-resistant species E. grandis. These studies involved seedlings but adult material was also used when checking the association between frost resistance and G, the growth regulator in E. grandis. Provided that night temperatures were close to freezing, rapid hardening was independent of photoperiod, light source and day/night temperature differentials. No significant relationship between level of frost resistance and intensity of leaf glaucousness was observed in a segregating progeny of E. urnigera. In F2 and backcross progenies between E. pulverulenta and E. grandis, no evidence was obtained for either physiological or genetical links between glaucousness and frost resistance. As in several other Eucalyptus species, low root temperatures delayed rapid dehardening in E. grandis. Increased frost resistance towards the top of E. grandis seedlings was associated with marked ontogenetic increases in G content. The G content of a 2 m sapling was highest in winter when maximum frost resistance had developed. This and other supporting evidence suggests that G has a role in the frost resistance of E. Grandis perhaps by affecting active electron transport properties of membranes. No information of this kind is available for other Eucalyptus species.

scholarly journals A survey of graph coloring - its types, methods and applications

2012 ◽  
Vol 37 (3) ◽  
pp. 223-238 ◽  
Author(s):  
Piotr Formanowicz ◽  
Krzysztof Tanaś
Keyword(s):  
Graph Theory ◽  
Graph Coloring ◽  
Cubic Graphs ◽  
The World ◽  
Computer Scientists

Abstract Graph coloring is one of the best known, popular and extensively researched subject in the field of graph theory, having many applications and conjectures, which are still open and studied by various mathematicians and computer scientists along the world. In this paper we present a survey of graph coloring as an important subfield of graph theory, describing various methods of the coloring, and a list of problems and conjectures associated with them. Lastly, we turn our attention to cubic graphs, a class of graphs, which has been found to be very interesting to study and color. A brief review of graph coloring methods (in Polish) was given by Kubale in [32] and a more detailed one in a book by the same author. We extend this review and explore the field of graph coloring further, describing various results obtained by other authors and show some interesting applications of this field of graph theory.

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