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Pm□Pn的奇染色和正常无冲突染色
Odd Coloring and Proper Conflict-Free Coloring of Pm□Pn

DOI: 10.12677/pm.2025.151024, PP. 211-215

Keywords: 路，笛卡尔乘积图，奇染色，正常无冲突染色
Path, Cartesian Product Graph, Odd Coloring, Proper Conflict-Free Coloring

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Abstract:

图的染色理论在模式识别、生物信息、社交网络和电力网络上有重要的应用。对于图 G 的一个点染色 φ:V( G )→{ 1,2,？,k } ，若满足对任意非孤立点 v∈V( G ) ，都存在 c∈{ 1,2,？,k } 使得 | φ ？1 ( c )∩N( v ) | 是一个奇数，则称 φ 是图 G 的一个奇 k -染色。特别地，若 | φ ？1 ( c )∩N( v ) |=1 ，则称 φ 是图 G 的一个正常无冲突 k -染色。图 G 的奇(正常无冲突)色数是使图 G 有一个奇(正常无冲突) k -染色的 k 的最小值，记作 χ o ( G )(

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