2018/06/18 by Pu Qiao, Qiao, Pu, Xingzhi Zhan +1
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.1806.06564
openalex publication_date 2018/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A detour of a graph G is a longest path in G. The detour order of G is the number of vertices in a detour of G. A graph is said to be detour-saturated if the addition of any edge increases strictly the detour order. L.W. Beineke, J.E. Dunbar and M. Frick asked the following three questions in 2005. (1) What is the smallest order of a detour-saturated graph of girth 4? (2) Let Pr be the graph obtained from the Petersen graph by splitting one of its vertices into three leaves. Is Pr the smallest triangle-free detour-saturated graph? (3) Does there exist a detour-saturated graph with finite girth bigger than 5? We answer these questions.