Rainbow matching in edge-colored graphs.
LeSaulnier, Timothy D., Stocker, Christopher, Wenger, Paul S., West, Douglas B. (2010)
The Electronic Journal of Combinatorics [electronic only]
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Displaying similar documents to “On -edge cover coloring of nearly bipartite graphs.”
Rainbow matching in edge-colored graphs.
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', Daniel, Norine, Serguei, Thomas, Robin (2006)
The Electronic Journal of Combinatorics [electronic only]
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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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A rainbow -matching in the complete graph with colors.
Fujita, Shinya, Kaneko, Atsushi, Schiermeyer, Ingo, Suzuki, Kazuhiro (2009)
The Electronic Journal of Combinatorics [electronic only]
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Adjacent vertex distinguishing edge-colorings of planar graphs with girth at least six
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,...
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 ∆.
On Twin Edge Colorings of Graphs
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
A Note on Neighbor Expanded Sum Distinguishing Index
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.
Edge-coloring and -coloring for various classes of graphs.
Zhou, Xiao, Nishizeki, Takao (1999)
Journal of Graph Algorithms and Applications
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Coloring with no 2-colored '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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Antiflows, oriented and strong oriented colorings of graphs
Robert Šámal (2004)
Archivum Mathematicum
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We present an overview of the theory of nowhere zero flows, in particular the duality of flows and colorings, and the extension to antiflows and strong oriented colorings. As the main result, we find the asymptotic relation between oriented and strong oriented chromatic number.