2023/01/16 by Samvel Kh. Darbinyan, Darbinyan, Samvel Kh. · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2301.06361
openalex publication_date 2023/01/16 · openalex created_date 2023/01/19 · openalex updated_date 2026/07/28
Let G be a strongly connected directed graph of order p≥ 3. In this paper, we show that if d(x)+d(y)≥ 2p-2 (respectively, d(x)+d(y)≥ 2p-1) for every pair of non-adjacent vertices x, y, then G contains a Hamiltonian path (with only a few exceptional cases that can be clearly characterized) in which the initial vertex dominates the terminal vertex (respectively, G contains two distinct verteces x and y such that there are two internally disjoint (x,y)-paths of lengths p-2 and 2).