2024/06/22 by Changchang Dong, Dong, Changchang, Jixiang Meng +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2406.15841
openalex publication_date 2024/06/22 · openalex created_date 2024/06/26 · openalex updated_date 2026/07/28
A digraph D is supereulerian if D contains a spanning eulerian subdigraph. For any two vertices u,v in a digraph D, if (u,w),(v,w)∈ A(D) for some w∈ V(D), then we call the pair \u, v\ dominating; if (w,u),(w,v)∈ A(D) for some w∈ V(D), then we call the pair \u, v\ dominated. In 2015, Bang-Jensen and Maddaloni [Journal of graph theory, 79(1) (2015) 8-20] proved that if a strong digraph D with n vertices satisfies d(u) + d(v)≥ 2n -3 for any pair of nonadjacent vertices \u,v\ of D, then D is supereulerian. In this paper, we study the above degree sum condition for any pair of dominated or dominating nonadjacent vertices of supereulerian digraphs.