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

2015/06/12 by Keaitsuda Maneeruk Nakprasit, Nakprasit, Keaitsuda Maneeruk, Kittikorn Nakprasit +1
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1506.03913

openalex publication_date 2015/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A (q,r)\-tree-coloring of a graph G is a q-coloring of vertices\nof G such that the subgraph induced by each color class is a forest of\nmaximum degree at most r. An \equitable (q, r)-tree-coloring of a\ngraph G is a (q,r)-tree-coloring such that the sizes of any two color\nclasses differ by at most one. Let the \strong equitable vertex\nr-arboricity be the minimum p such that G has an equitable (q,\nr)-tree-coloring for every q\≥ p.\n In this paper, we find the exact value for each va^\≡₂(K_m,n) and\nva^\≡₂(K_l,m,n).\n

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