树和路字典积图的线性荫度

Linear Arboricity of Lexicographic Products of Trees and Paths

近期,李确定了树Tm和路Pn的笛卡尔积图TmWPn、直积图Tm×Pn、强积图Tm)Pn的线性荫度,但其证明中漏掉了n=2的情况。本文先对以上三个乘积图的线性荫度补充n=2的证明,然后计算树和完全图的直积图以及树和路、路和树字典积图的线性荫度。

Li has determined the linear arboricities of Cartesian product graph TmWPn , direct product graph Tm×Pn , and strong product graph Tm)Pn of tree Tm and path Pn recently, but their proofs left out the case n=2 . In this paper, we first supplement the proofs of n=2 to the linear arboricities of the above three product graphs, then we calculate the linear arboricities of the direct product of tree and complete graph, and the lexicographic products of tree and path and path and tree.