Generalizations of the classics to spanning connectedness

Eminjan Sabir and Jixiang Meng

Applied Mathematics and Computation, 2021, vol. 403, issue C

Abstract: Let G=(V,E) be a graph and u,v be two arbitrary vertices of V(G). Then G is hamilton-connected if there exists a spanning path between u and v, and G is hamiltonian if there exist two internally disjoint pathes between u and v and the union of these two paths spans V(G). More generally, G is said to be spanningk-connected if there exist k internally disjoint pathes between u and v and the union of these k pathes contains all vertices of G. In the paper, we first generalize a classic theorem of Vergnas on hamiltonian graphs to spanning k-connectedness. Furthermore, we determine extremal number of edges in a spanning k-connected graph by extending an old theorem due to Erdős. Finally, we partially establish spanning k-connected versions of famous Chvátal-Erdős theorem.

Keywords: Hamiltonicity; Spanning connectedness; Extremal problem; Chvátal-Erdős theorem (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:403:y:2021:i:c:s0096300321002575

DOI: 10.1016/j.amc.2021.126167

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