Affiliation:
1. School of Mathematical Sciences Dalian University of Technology Dalian Liaoning China
2. Department of Mathematics and Statistics Georgia State University Atlanta Georgia USA
3. School of Mathematical and Data Sciences West Virginia University Morgantown West Virginia USA
4. Department of Mathematics and Statistics Auburn University Auburn Alabama USA
Abstract
AbstractLet be a simple graph. Let and be the maximum degree and the chromatic index of , respectively. We call overfull if , and critical if for every proper subgraph of . Clearly, if is overfull then . The core of , denoted by , is the subgraph of induced by all its maximum degree vertices. We believe that utilizing the core degree condition could be considered as an approach to attack the overfull conjecture. Along this direction, we in this paper show that for any integer , if is critical with and , then is overfull.
Funder
Division of Mathematical Sciences
Subject
Geometry and Topology,Discrete Mathematics and Combinatorics
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