2018/12/05 by Ruijuan Li, Li, Ruijuan, Juanjuan Liang +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1812.01800
openalex publication_date 2018/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Sullivan stated the conjectures: (1) every oriented graph D has a vertex x such that d++(x)≥ d-(x); (2) every oriented graph D has a vertex x such that d++(x)+d+(x)≥ 2d-(x). In this paper, we prove that these conjectures hold for local tournaments. In particular, for a local tournament D, we prove that D has at least two vertices satisfying (1) if D has no vertex of in-degree zero. And, for a local tournament D, we prove that either there exist two vertices satisfying (2) or there exists a vertex v satisfying d++(v)+d+(v)≥ 2d-(v)+2 if D has no vertex of in-degree zero.