Abstract. We give a simpler proof of the theorem due to B. Jackson and Y. Zhu, Z. Liu, and Z. Yu that, except for the Petersen graph, every 2-connected k- ...
It is essentially best possible for k > 4 since there exist non-hamiltonian, 2-connected, k- regular graphs on 3k + 4 vertices for k even, and 3k + 5 vertices ...
P. Erdös and A. M. Hobbs, Hamilton cycles in regular graphs of moderate degree, J. Combinatorial Theory Ser. B, in press.
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Oct 28, 2015 · In a Hamiltonian graph there is a cycle containing all vertices. When you remove one vertex from this cycle, the remaining graph contains a path ...
Every 2-connected k-regulfu graph on at most 3k + 1 vertices is hamiltonian, except for the Petersen graph. The purpose of this paper is to present a simpler ...
Nov 1, 2023 · Let G be a 2-connected, k-regular graph on at most 3k-1 vertices, and let e = uv be any edge of G such that 1u, vl is not a cut-set. Then G has ...
Jun 22, 2016 · Remark: every 2-connected k-regular graph with at most 3k+3 vertices admits a Hamiltonian cycle or is one of the two exceptions, which admit a ...
The sufficiency is an immediate consequence of the following two results. Theorem 6. dominating cycle, then G is hamiltonian. Let G be a k-regular graph on at ...
Sep 24, 2010 · First step let assume the graph has even number of vertices. In the second stage, we will extend the construction, so that if k is even, ...
Feb 25, 2022 · Let P=uvz be a 2-path of a 2-connected, k-regular graph G on at most 2k vertices. In this paper, we show that there is a Hamiltonian cycle ...