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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Juvan, Martin, Mohar, Bojan, Thomas, Robin (1999)
The Electronic Journal of Combinatorics [electronic only]
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Ghebleh, Mohammad, Kral', Daniel, Norine, Serguei, Thomas, Robin (2006)
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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Yuehua Bu, Ko-Wei Lih, Weifan Wang (2011)
Discussiones Mathematicae Graph Theory
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An adjacent vertex distinguishing edge-coloring of a graph G is a proper edge-coloring o G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by χ'ₐ(G). We prove that χ'ₐ(G) is at most the maximum degree plus 2 if G is a planar graph without isolated edges whose girth is at least 6. This gives new evidence to a conjecture proposed in [Z. Zhang, L. Liu,...
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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Loh, Po-Shen (2009)
The Electronic Journal of Combinatorics [electronic only]
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Mohar, Bojan, Pisanski, Tomaz (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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Sylwia Cichacz, Jakub Przybyło (2010)
Discussiones Mathematicae Graph Theory
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In the PhD thesis by Burris (Memphis (1993)), a conjecture was made concerning the number of colors c(G) required to edge-color a simple graph G so that no two distinct vertices are incident to the same multiset of colors. We find the exact value of c(G) - the irregular coloring number, and hence verify the conjecture when G is a vertex-disjoint union of paths. We also investigate the point-distinguishing chromatic index, χ₀(G), where sets, instead of multisets, are required to be distinct,...
Dzido, Tomasz, Nowik, Andrzej, Szuca, Piotr (2005)
The Electronic Journal of Combinatorics [electronic only]
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Yuster, Raphael (2006)
The Electronic Journal of Combinatorics [electronic only]
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Eric Andrews, Laars Helenius, Daniel Johnston, Jonathon VerWys, Ping Zhang (2014)
Discussiones Mathematicae Graph Theory
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A twin edge k-coloring of a graph G is a proper edge coloring of G with the elements of Zk so that the induced vertex coloring in which the color of a vertex v in G is the sum (in Zk) of the colors of the edges incident with v is a proper vertex coloring. The minimum k for which G has a twin edge k-coloring is called the twin chromatic index of G. Among the results presented are formulas for the twin chromatic index of each complete graph and each complete bipartite graph
Evelyne Flandrin, Hao Li, Antoni Marczyk, Jean-François Saclé, Mariusz Woźniak (2017)
Discussiones Mathematicae Graph Theory
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A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set [k] = {1, . . . , k}. These colors can be used to distinguish the vertices of G. There are many possibilities of such a distinction. In this paper, we consider the sum of colors on incident edges and adjacent vertices.
Gyárfás, András, Ruszinkó, Miklós, Sarközy, Gábor N., Szemerédi, Endre (2011)
The Electronic Journal of Combinatorics [electronic only]
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