2008/01/01 by Xueliang Li, Fengxia Liu, Li, Xueliang +1
Computer Science · Mathematics · #05C05 #05C15 #05C35 #05C70 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.0801.0270
openalex publication_date 2008/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The monochromatic tree partition number of an r-edge-colored graph G, denoted by tr(G), is the minimum integer k such that whenever the edges of G are colored with r colors, the vertices of G can be covered by at most k vertex-disjoint monochromatic trees. In general, to determine this number is very difficult. For 2-edge-colored complete multipartite graph, Kaneko, Kano, and Suzuki gave the exact value of t2(K(n1,n2,...,nk)). In this paper, we prove that if n≥ 3, and K(n,n) is 3-edge-colored such that every vertex has color degree 3, then t3(K(n,n))=3.