On the Equitable Coloring of Halin Graphs
碩士 === 國立臺灣大學 === 數學研究所 === 93 === A Halin graph is a planar graph consisting of a tree with no vertex of degree two and a cycly connecting the leaves of the tree. We write . A graph is said to be equitably -colorable if the vertices of is colored with colors such that there are no two adj...
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| Format: | Others |
| Language: | en_US |
| Published: |
2005
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| Online Access: | http://ndltd.ncl.edu.tw/handle/18355132191326757520 |
| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 93 === A Halin graph is a planar graph consisting of a tree with no vertex of degree two and a cycly connecting the leaves of the tree. We write . A graph is said to be equitably -colorable if the vertices of is colored with colors such that there are no two adjacent vertices of the same color and the size of the color classes differ by at most one. Let be the maximum degree of a vertex in graph . Chen et al. conjectured that a connected graph is equitable -colorable if is not a complete graph , or an odd cycle , or a complete bipartite graph for all . In this thesis, we prove that any Halin graph except has an equitable -coloring.
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