An improvement to the Hilton-Zhao vertex-splitting conjecture |
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Institution: | 1. Department of Mathematics, West Virginia University, Morgantown, WV 26506, United States of America;2. Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30302, United States of America;3. Department of Mathematics, Illinois State University, Normal, IL 61790, United States of America |
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Abstract: | For a simple graph G, denote by n, , and its order, maximum degree, and chromatic index, respectively. A graph G is edge-chromatic critical if and for every proper subgraph H of G. Let G be an n-vertex connected regular class 1 graph, and let be obtained from G by splitting one vertex of G into two vertices. Hilton and Zhao in 1997 conjectured that must be edge-chromatic critical if , and they verified this when . In this paper, we prove it for . |
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Keywords: | Overfull graph Multifan Kierstead path Vertex-splitting |
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