4 research outputs found
Research on Necessary and Sufficient Condition for Hamilton Graph
AbstractAn important concept, “closed domain” is proposed in this paper. In the same time, necessary and sufficient lemma for closed domain, R, is proved on which necessary and sufficient theorem for judging whether a general graph G is a Hamilton graph is proposed and proved. All instances in this paper are judged by comparatively using the theorem proposed herein and the original necessary condition theorem and sufficient condition theorem to prove the correctness of the method proposed in this paper
Neighborhood intersections and Hamiltonicity in almost claw-free graphs
AbstractLet G be a graph. The partially square graph G∗ of G is a graph obtained from G by adding edges uv satisfying the conditions uv∉E(G), and there is some w∈N(u)∩N(v), such that N(w)⊆N(u)∪N(v)∪{u,v}. Let t>1 be an integer and Y⊆V(G), denote n(Y)=|{v∈V(G)|miny∈Y{distG(v,y)}⩽2}|,It(G)={Z|Z is an independent set of G,|Z|=t}. In this paper, we show that a k-connected almost claw-free graph with k⩾2 is hamiltonian if ∑z∈Zd(z)⩾n(Z)−k in G for each Z∈Ik+1(G∗), thereby solving a conjecture proposed by Broersma, Ryjác̆ek and Schiermeyer. Zhang's result is also generalized by the new result
Portland Daily Press: July 23, 1878
https://digitalmaine.com/pdp_1878/1170/thumbnail.jp