Graph Edge Coloring: A Survey
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DOI: 10.1007/s00373-018-1986-5
Abstract: Graph edge coloring has a rich theory, many applications and beautiful conjectures, and it is studied not only by mathematicians, but also by computer scientists. In this survey, written for the non-expert, we shall describe… read more here.
Keywords: graph edge; edge coloring; coloring survey;
A Structure of 1-Planar Graph and Its Applications to Coloring Problems
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DOI: 10.1007/s00373-019-02027-0
Abstract: A graph is 1-planar if it can be drawn on a plane so that each edge is crossed by at most one other edge. In this paper, we first give a useful structural theorem for… read more here.
Keywords: list; graph; edge coloring; planar graph ... See more keywords
Magic Labeling of Disjoint Union Graphs
Sign Up to like & getrecommendations! Published in 2019 at "Acta Mathematica Sinica, English Series"
DOI: 10.1007/s10114-019-8500-8
Abstract: Let G be a graph with vertex set V(G), edge set E(G) and maximum degree Δ respectively. G is called degree-magic if it admits a labelling of the edges by integers {1, 2, …, |E(G)|}… read more here.
Keywords: labeling disjoint; edge; graph; edge coloring ... See more keywords
An exact algorithm for the edge coloring by total labeling problem
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DOI: 10.1007/s10479-018-2977-x
Abstract: This paper addresses the edge coloring by total labeling graph problem. This is a labeling of the vertices and edges of a graph such that the weights (colors) of the edges, defined by the sum… read more here.
Keywords: problem; coloring total; algorithm; edge coloring ... See more keywords
Anti-Ramsey coloring for matchings in complete bipartite graphs
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DOI: 10.1007/s10878-015-9926-2
Abstract: The anti-Ramsey number AR(G, H) is defined to be the maximum number of colors in an edge coloring of G which doesn’t contain any rainbow subgraphs isomorphic to H. It is clear that there is an… read more here.
Keywords: ramsey coloring; anti ramsey; anti; edge coloring ... See more keywords
Adjacent Vertex Distinguishing Edge Coloring of Planar Graphs Without 4-Cycles
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DOI: 10.1007/s40840-019-00860-3
Abstract: The adjacent vertex distinguishing edge coloring of a graph G is a proper edge coloring of G such that the edge coloring set on any pair of adjacent vertices is distinct. The minimum number of… read more here.
Keywords: vertex distinguishing; adjacent vertex; edge; edge coloring ... See more keywords
Edge-Coloring Technique to Analyze Elementary Trapping Sets of Spatially-Coupled LDPC Convolutional Codes
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DOI: 10.1109/lcomm.2019.2962671
Abstract: In this letter, for the first time, an edge-coloring technique is proposed to characterize a certain elementary trapping set (ETS) and to obtain sufficient conditions to avoid small ETSs from occurrence in the Tanner graph… read more here.
Keywords: coloring technique; convolutional codes; ldpc convolutional; elementary trapping ... See more keywords
Facial rainbow edge-coloring of simple 3-connected plane graphs
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DOI: 10.7494/opmath.2020.40.4.475
Abstract: A facial rainbow edge-coloring of a plane graph \(G\) is an edge-coloring such that any two edges receive distinct colors if they lie on a common facial path of \(G\). The minimum number of colors… read more here.
Keywords: rainbow edge; edge coloring; facial rainbow; text ... See more keywords