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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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Facial graceful coloring of plane graphs [PDF]
Opuscula MathematicaLet \(G\) be a plane graph. Two edges of \(G\) are facially adjacent if they are consecutive on the boundary walk of a face of \(G\). A facial edge coloring of \(G\) is an edge coloring such that any two facially adjacent edges receive different colors ...
Július Czap
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Improved Bounds for Some Facially Constrained Colorings
Discussiones Mathematicae Graph Theory, 2023 A facial-parity edge-coloring of a 2-edge-connected plane graph is a facially-proper edge-coloring in which every face is incident with zero or an odd number of edges of each color. A facial-parity vertex-coloring of a 2-connected plane graph is a proper
Štorgel Kenny
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A structural approach to the graceful coloring of a subclass of trees
Heliyon, 2023 Let M={1,2,..m} and G be a simple graph. A graceful m-coloring of G is a proper vertex coloring of G using the colors in M which leads to a proper edge coloring using M∖{m} colors such that the associated color of each edge is the absolute difference ...
Laavanya D, Devi Yamini S
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Acyclicity in edge-colored graphs
Discrete Mathematics, 2017 A walk $W$ in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in $W$ is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type $i$ is a proper superset of graphs of acyclicity of type $i+1$, $i=1,2,3,4.$ The first three types are ...
Gregory Z. Gutin +4 more
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Degenerate matchings and edge colorings [PDF]
Discrete Applied Mathematics, 2018 A matching $M$ in a graph $G$ is $r$-degenerate if the subgraph of $G$ induced by the set of vertices incident with an edge in $M$ is $r$-degenerate. Goddard, Hedetniemi, Hedetniemi, and Laskar (Generalized subgraph-restricted matchings in graphs, Discrete Mathematics 293 (2005) 129-138) introduced the notion of acyclic matchings, which coincide with ...
Baste, Julien, Rautenbach, Dieter
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On the Star Chromatic Index of Generalized Petersen Graphs
Discussiones Mathematicae Graph Theory, 2021 The star k-edge-coloring of graph G is a proper edge coloring using k colors such that no path or cycle of length four is bichromatic. The minimum number k for which G admits a star k-edge-coloring is called the star chromatic index of G, denoted by χ′s (
Zhu Enqiang, Shao Zehui
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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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Edge-Coloring Bipartite Graphs [PDF]
Journal of Algorithms, 2000 This note provides an algorithm for finding \(\Delta\)(colors)-edge-coloring of a bipartite graph of order \(n\) and size \(m\) in time \(T+O(m\log \Delta)\) where \(T\) is the time needed to find a perfect matching in a \(k\)-regular bipartite graph, \(k\leq \Delta\), and \(\Delta\) is the maximum degree of vertices.
Ajai Kapoor, Romeo Rizzi
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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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