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arXiv · 1506.03913

The strong equitable vertex 2-arboricity of complete bipartite and tripartite graphs

Keaitsuda Maneeruk Nakprasit·Kittikorn Nakprasit
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Abstract

A $(q,r)$\emph{-tree-coloring} of a graph $G$ is a $q$-coloring of vertices of $G$ such that the subgraph induced by each color class is a forest of maximum degree at most $r.$ An \emph{equitable $(q, r)$-tree-coloring} of a graph $G$ is a $(q,r)$-tree-coloring such that the sizes of any two color classes differ by at most one. Let the \emph{strong equitable vertex $r$-arboricity} be the minimum $p$ such that $G$ has an equitable $(q, r)$-tree-coloring for every $q\geq p.$ In this paper, we find the exact value for each $va^\equiv_2(K_{m,n})$ and $va^\equiv_2(K_{l,m,n}).$

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Keaitsuda Maneeruk Nakprasit, Kittikorn Nakprasit. 2015-06-12. The strong equitable vertex 2-arboricity of complete bipartite and tripartite graphs. https://arxiv.org/abs/1506.03913

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