2017/09/05 by Zhenzhen Li, Li, Zhenzhen, Baoyindureng Wu +1 · 2 citations
Computer Science · Mathematics · #05C05 #05C15 #05D05 #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.1709.01225
openalex publication_date 2017/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A path in a vertex-colored graph is called \it conflict-free if there is a color used on exactly one of its vertices. A vertex-colored graph is said to be \it conflict-free vertex-connected if any two vertices of the graph are connected by a conflict-free path. The \it conflict-free vertex-connection number, denoted by vcfc(G), is defined as the smallest number of colors required to make G conflict-free vertex-connected. Li et al. conjectured that for a connected graph G of order n, vcfc(G)≤ vcfc(Pn). We confirm that the conjecture is true and pose a a relevant conjecture concerning the conflict-free connection number introduced by Czap et al..