| 彩春丽,易华.最大度较小的图的线性着色[J].井冈山大学自然版,2020,41(5):5-9 |
| 最大度较小的图的线性着色 |
| LINEAR COLORING OF GRAPHS WITH SMALL MAXIMUM DEGREE |
| 投稿时间：2020-04-20 修订日期：2020-05-18 |
| DOI：10.3969/j.issn.1674-8085.2020.05.002 |
| 中文关键词: 最大度 线性着色 线性色数 |
| 英文关键词: maximum degree linear coloring linear chromatic number |
| 基金项目: |
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| 摘要点击次数: 1320 |
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| 中文摘要: |
| 本文研究了最大度较小的图的线性着色问题。通过分析未着色顶点的邻近顶点的着色情况，扩充图的部分线性着色，利用数学归纳法证明了△（G）≤4的非4正则图G的线性色数有lc（G）≤7和△（G）≤5的非5正则图G的线性色数有lc（G）≤13。 |
| 英文摘要: |
| we studied the problem of linear coloring of graphs with small maximum degree. By analyzing the coloring of the vertices with distance at most 2 from the uncolored vertex， extending the partial linear coloring of graph to the whole graph, and usingmathematical induction, we proved that lc(G) ≤ 7 if G is not4-regular graph with △(G)≤ 4, and lc(G) ≤ 13 if G is not5-regular graph with △(G)≤ 5. |
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