| 彩春丽,陶黄林,彭嘉昊.围长至少为5的平面图的线性着色[J].井冈山大学自然版,2021,42(3):8-11,19 |
| 围长至少为5的平面图的线性着色 |
| LINEAR COLORING OF PLANAR GRAPHS WITH GIRTH AT LEAST 5 |
| 投稿时间：2021-01-09 修订日期：2021-02-19 |
| DOI：10.3669/j.issn.1674-8085.2021.03.002 |
| 中文关键词: 围长 平面图 线性着色 线性色数 |
| 英文关键词: girth planar graphs linear coloring linear chromatic number |
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| 中文摘要: |
| 本文研究了围长至少为5的平面图的线性着色问题。利用反证法，通过分析最小反例图的结构，运用欧拉公式结合适当的权转移规则得出矛盾，从而证明了围长至少为5的平面图的线性色数满足lc（G）≤[△（G）/2]+4，改进了这方面的结果。 |
| 英文摘要: |
| The problem of linear coloring of planar graphs with girth at least 5 was studied. By using the method of counter-evidence, though analyzing the configurations of a minimal counterexample, and applying Euler's formula with appropriate discharging rules to obtain a contradiction, thus demonstrating lc(G) ≤ [△(G)/2]+4 for planar graph with girth at least 5. The results have been improved in this regard. |
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