Antiflows, oriented and strong oriented colorings of graphs

Robert Šámal

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Displaying similar documents to “Antiflows, oriented and strong oriented colorings of graphs”

Analogues of cliques for oriented coloring

William F. Klostermeyer, Gary MacGillivray (2004)

Discussiones Mathematicae Graph Theory

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We examine subgraphs of oriented graphs in the context of oriented coloring that are analogous to cliques in traditional vertex coloring. Bounds on the sizes of these subgraphs are given for planar, outerplanar, and series-parallel graphs. In particular, the main result of the paper is that a planar graph cannot contain an induced subgraph D with more than 36 vertices such that each pair of vertices in D are joined by a directed path of length at most two.

Precise Upper Bound for the Strong Edge Chromatic Number of Sparse Planar Graphs

Oleg V. Borodin, Anna O. Ivanova (2013)

Discussiones Mathematicae Graph Theory

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We prove that every planar graph with maximum degree ∆ is strong edge (2∆−1)-colorable if its girth is at least 40 [...] +1. The bound 2∆−1 is reached at any graph that has two adjacent vertices of degree ∆.

Strong Edge-Coloring Of Planar Graphs

Wen-Yao Song, Lian-Ying Miao (2017)

Discussiones Mathematicae Graph Theory

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A strong edge-coloring of a graph is a proper edge-coloring where each color class induces a matching. We denote by 𝜒's(G) the strong chromatic index of G which is the smallest integer k such that G can be strongly edge-colored with k colors. It is known that every planar graph G has a strong edge-coloring with at most 4 Δ(G) + 4 colors [R.J. Faudree, A. Gyárfás, R.H. Schelp and Zs. Tuza, The strong chromatic index of graphs, Ars Combin. 29B (1990) 205–211]. In this paper, we show that...

On $f$ -edge cover coloring of nearly bipartite graphs.

Li, Jinbo, Liu, Guizhen (2011)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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Coloring with no 2-colored $P_{4}$ 's.

Albertson, Michael O., Chappell, Glenn G., Kierstead, H.A., Kündgen, André, Ramamurthi, Radhika (2004)

The Electronic Journal of Combinatorics [electronic only]

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M 2 -Edge Colorings Of Cacti And Graph Joins

Július Czap, Peter Šugerek, Jaroslav Ivančo (2016)

Discussiones Mathematicae Graph Theory

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An edge coloring φ of a graph G is called an M2-edge coloring if |φ(v)| ≤ 2 for every vertex v of G, where φ(v) is the set of colors of edges incident with v. Let 𝒦2(G) denote the maximum number of colors used in an M2-edge coloring of G. In this paper we determine 𝒦2(G) for trees, cacti, complete multipartite graphs and graph joins.

The circular chromatic index of flower snarks.

Ghebleh, Mohammad, Kral&amp;#039;, Daniel, Norine, Serguei, Thomas, Robin (2006)

The Electronic Journal of Combinatorics [electronic only]

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Edge-coloring and $f$ -coloring for various classes of graphs.

Zhou, Xiao, Nishizeki, Takao (1999)

Journal of Graph Algorithms and Applications

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Edge-coloring of a family of regular graphs.

Mohar, Bojan, Pisanski, Tomaz (1983)

Publications de l'Institut Mathématique. Nouvelle Série

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Sum List Edge Colorings of Graphs

Arnfried Kemnitz, Massimiliano Marangio, Margit Voigt (2016)

Discussiones Mathematicae Graph Theory

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Let G = (V,E) be a simple graph and for every edge e ∈ E let L(e) be a set (list) of available colors. The graph G is called L-edge colorable if there is a proper edge coloring c of G with c(e) ∈ L(e) for all e ∈ E. A function f : E → ℕ is called an edge choice function of G and G is said to be f-edge choosable if G is L-edge colorable for every list assignment L with |L(e)| = f(e) for all e ∈ E. Set size(f) = ∑e∈E f(e) and define the sum choice index χ′sc(G) as the minimum of size(f)...

List edge-colorings of series-parallel graphs.

Juvan, Martin, Mohar, Bojan, Thomas, Robin (1999)

The Electronic Journal of Combinatorics [electronic only]

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Interval Edge-Colorings of Cartesian Products of Graphs I

Petros A. Petrosyan, Hrant H. Khachatrian, Hovhannes G. Tananyan (2013)

Discussiones Mathematicae Graph Theory

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A proper edge-coloring of a graph G with colors 1, . . . , t is an interval t-coloring if all colors are used and the colors of edges incident to each vertex of G form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. Let [...] be the set of all interval colorable graphs. For a graph G ∈ [...] , the least and the greatest values of t for which G has an interval t-coloring are denoted by w(G) and W(G), respectively....