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Grünbaum colorings extended to non-facial 3-cycles
Electronic Journal of Graph Theory and Applications, 2022 We consider the question of when a triangulation with a Grünbaum coloring can be edge-colored with three colors such that the non-facial 3-cycles also receive all three colors; we will call this a strong Grünbaum coloring.
sarah-marie belcastro, Ruth Haas
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Journal of Combinatorial Theory, Series B, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Paul N. Balister +3 more
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Some Equal Degree Graph Edge Chromatic Number
MATEC Web of Conferences, 2016 Let G(V, E) be a simple graph and k is a positive integer, if it exists a mapping of f, and satisfied with f(e1)≠6 = f(e2) for two incident edges e1,e2∉E(G), f(e1)≠6=f(e2), then f is called the k-proper-edge coloring of G(k-PEC for short).
Liu Jun +4 more
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Normal 5-edge-colorings of a family of Loupekhine snarks
AKCE International Journal of Graphs and Combinatorics, 2020 In a proper edge-coloring of a cubic graph an edge uv is called poor or rich, if the set of colors of the edges incident to u and v contains exactly three or five colors, respectively.
Luca Ferrarini +2 more
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Electronic Notes in Discrete Mathematics, 2008 Abstract A split graph is a graph whose vertex set admits a partition into a stable set and a clique. The chromatic indexes for some subsets of split graphs, such as split graphs with odd maximum degree and split-indifference graphs, are known. However, for the general class, the problem remains unsolved.
S. M. ALMEIDA +2 more
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A note on edge colorings and trees
Mathematical Logic Quarterly, 2022 AbstractWe point out some connections between existence of homogenous sets for certain edge colorings and existence of branches in certain trees. As a consequence, we get that any locally additive coloring (a notion introduced in the paper) of a cardinal κ has a homogeneous set of size κ provided that the number of colors μ satisfies .
Adi Jarden, Ziv Shami
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M_{2}-edge colorings of dense graphs [PDF]
Opuscula Mathematica, 2016 An edge coloring \(\varphi\) of a graph \(G\) is called an \(\mathrm{M}_i\)-edge coloring if \(|\varphi(v)|\leq i\) for every vertex \(v\) of \(G\), where \(\varphi(v)\) is the set of colors of edges incident with \(v\).
Jaroslav Ivančo
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Algorithmica, 2016 A b-coloring of the vertices of a graph is a proper coloring where each color class contains a vertex which is adjacent to at least one vertex in each other color class. The b-chromatic number of $G$ is the maximum integer $b(G)$ for which $G$ has a b-coloring with $b(G)$ colors.
Victor Campos, FERREIRA DA SILVA A
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On star and biclique edge‐colorings [PDF]
International Transactions in Operational Research, 2016 AbstractA biclique of G is a maximal set of vertices that induces a complete bipartite subgraph of G with at least one edge, and a star of a graph G is a maximal set of vertices that induces a complete bipartite graph . A biclique (resp. star) edge‐coloring is a coloring of the edges of a graph with no monochromatic bicliques (resp. stars).
Simone Dantas +5 more
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On the Adjacent Strong Equitable Edge Coloring of Pn ∨ Pn, Pn ∨ Cn and Cn ∨ Cn
MATEC Web of Conferences, 2016 A proper edge coloring of graph G is called equitable adjacent strong edge coloring if colored sets from every two adjacent vertices incident edge are different,and the number of edges in any two color classes differ by at most one,which the required ...
Liu Jun +4 more
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