K_(n)□K_(m,s)的r-hued染色  

r-Hued Coloring of K_(n)□K_(m,s)

作　　者：梁玲梅 刘凤霞[1] 赖虹建[2] LIANG Lingmei;LIU Fengxia;LAI Hongjian(College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,China;Department of Mathematics,West Virginia University,Morgantown 26506,West Virginia,USA)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046 [2]西弗吉尼亚大学数学系,美国西弗吉尼亚摩根城26506

出　　处：《吉林大学学报（理学版）》2023年第1期85-93,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11961067)。

摘　　要：考虑完全图K_(n)和完全二部图K_(m,s)的笛卡尔乘积图的r-hued色数.首先,根据正整数r的不同值进行分类,并结合K_(n)□K_(m,s)的性质,刻画该图r-hued色数的下界;其次,找到K_(n)□K_(m,s)的一个具体的(k,r)-染色,并以此刻画该图r-hued色数的一个上界;最后,确定了K_(n)□K_(m,s)的r-hued色数.We considered the r-hued chromatic number of Cartesian product of complete graph K_(n)and complete bipartite graph K_(m,s).Firstly,we classified the positive integer r according to its different values,and combined with the properties of K_(n)□K_(m,s),we characterized a lower bound of the r-hued chromatic number of the graph.Secondly,we found a specific(k,r)-coloring of K_(n)□K_(m,s),so we characterized an upper bound of the r-hued chromatic number of the graph.Finally,we determined the r-hued chromatic number of K_(n)□K_(m,s).

关 键 词：(k r)-染色 r-hued色数 笛卡尔乘积图 

分 类 号：O157.5[理学—数学]