P<sub>m</sub>~2×P<sub>n</sub>的r-多彩着色

张春梅; 史雅馨; 李越锋

doi:10.13568/j.cnki.651094.651316.2023.03.06.0001

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P_m~2×P_n的r-多彩着色

更新时间：2026-01-21

- P_m~2×P_n的r-多彩着色
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 40, Issue 6, Pages: 663-670(2023)
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2023.03.06.0001
  CLC： O157.5
- Published：2023
- 稿件说明：
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[1]张春梅,史雅馨,李越锋.P_m~2×P_n的r-多彩着色[J].新疆大学学报(自然科学版)(中英文),2023,40(06):663-670.
[1]张春梅,史雅馨,李越锋.P_m~2×P_n的r-多彩着色[J].新疆大学学报(自然科学版)(中英文),2023,40(06):663-670. DOI： 10.13568/j.cnki.651094.651316.2023.03.06.0001.

DOI：10.13568/j.cnki.651094.651316.2023.03.06.0001.

摘要

图G的(k

r)-着色是图G的一个正常k-着色

并满足G中的每一个顶点的邻点的颜色数至少为这个顶点的度d(v)和r的最小值.使得图G有(k

r)-着色的最小整数k称为图G的r-多彩色数

用χr(G)表示.研究了路的平方图和路的直积图的r-多彩着色

得到了r-多彩着色数.

Abstract

A(k

r)-coloring of G is a proper coloring with k colors such that for every vertex v with degree d(v) in G

the color number of the neighbors of v is at least min{d(v)

r}. The smallest integer k such that G has an(k

r)-coloring is called the r-hued chromatic number and denoted by χr(G). In this paper

we study the r-hued coloring of direct product of path with the square of path

and obtain its r-hued chromatic number.

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references

CHEN Y, FAN S H, LAI H J, et al. On dynamic coloring for planar graphs and graphs of higher genus[J]. Discrete Applied Mathematics, 2012, 160(7/8):1064-1071.

LAI H J, LIN J L, MONTGOMERY B, et al. Conditional colorings of graphs[J]. Discrete Math, 2006, 306(16):1997-2004.

DEEPA T, VENKATACHALAM M, FALCONR M, et al. On the r-dynamic coloring of the direct product of a path with either a path or a cycle[J]. AIMS Math, 2020, 5(6):6496-6520.

MONTGOMERY B. Dynamic coloring of graphs[D]. Morgantwon:West Virginia University, 2001.

LAI H J, MONTGOMERY B, POON H. Upper bounds of dynamic chromatic number[J]. Ars Combinatoria:An AustralianCanadian Journal of Combinatorics, 2003, 68:193-201.

AKBARI S, GHANBARI M, JAHANBEKAM S. On the list dynamic coloring of graphs[J]. Discrete Applied Mathematics, 2009,157(14):3005-3007.

刘丙雪,刘凤霞．笛卡儿积图的2-hued列表染色[J].新疆大学学报(自然科学版)(中英文), 2023, 40(1):30-35.

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Pm~2×Pn的r-多彩着色

DOI：10.13568/j.cnki.651094.651316.2023.03.06.0001

摘要

Abstract

关键词

Keywords

references

P_m~2×P_n的r-多彩着色