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Generalizations of the classics to spanning connectedness

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  • Sabir, Eminjan
  • Meng, Jixiang

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.

Suggested Citation

  • Sabir, Eminjan & Meng, Jixiang, 2021. "Generalizations of the classics to spanning connectedness," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    • Handle: RePEc:eee:apmaco:v:403:y:2021:i:c:s0096300321002575
    DOI: 10.1016/j.amc.2021.126167
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    1. Sabir, Eminjan & Meng, Jixiang, 2020. "Sufficient conditions for graphs to be spanning connected," Applied Mathematics and Computation, Elsevier, vol. 378(C).
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