Edge-coloring of a family of regular graphs.
Mohar, Bojan, Pisanski, Tomaz (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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Mohar, Bojan, Pisanski, Tomaz (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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Ghebleh, Mohammad, Kral', Daniel, Norine, Serguei, Thomas, Robin (2006)
The Electronic Journal of Combinatorics [electronic only]
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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 ∆.
Juvan, Martin, Mohar, Bojan, Thomas, Robin (1999)
The Electronic Journal of Combinatorics [electronic only]
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Zhou, Xiao, Nishizeki, Takao (1999)
Journal of Graph Algorithms and Applications
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LeSaulnier, Timothy D., Stocker, Christopher, Wenger, Paul S., West, Douglas B. (2010)
The Electronic Journal of Combinatorics [electronic only]
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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.
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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Schauz, Uwe (2010)
The Electronic Journal of Combinatorics [electronic only]
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Július Czap, Zsolt Tuza (2013)
Discussiones Mathematicae Graph Theory
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An edge coloring of a plane graph G is facially proper if no two faceadjacent edges of G receive the same color. A facial (facially proper) parity edge coloring of a plane graph G is an (facially proper) edge coloring with the property that, for each color c and each face f of G, either an odd number of edges incident with f is colored with c, or color c does not occur on the edges of f. In this paper we deal with the following question: For which integers k does there exist a facial...
Dzido, Tomasz, Nowik, Andrzej, Szuca, Piotr (2005)
The Electronic Journal of Combinatorics [electronic only]
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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....
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.
Yuster, Raphael (2006)
The Electronic Journal of Combinatorics [electronic only]
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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...