We strengthen the closure concept for Hamilton-connectedness in claw-free graphs,
introduced by the second and fourth authors, such that the strong closure GM of a claw-free …

Kuipers and Veldman conjectured that any 3-connected claw-free graph with order ν and
minimum degree δ⩾(ν+ 6) 10 is Hamiltonian for ν sufficiently large. In this paper, we prove …

An even cycle C in a graph G is a nice cycle if G− V (C) has a perfect matching. A graph G is
cycle-nice if each even cycle in G is a nice cycle. An even cycle C in an orientation of a …

We introduce a closure concept for hamiltonicity in the class of {K 1, 4, K 1, 4+ e}-free
graphs, extending the closure for claw-free graphs introduced by Ryjáček (1997)[18]. The …

We introduce a closure concept for a superclass of the class of claw-free graphs defined by
a degree condition on end vertices of induced claws. We show that the closure of a graph is …

Settling a conjecture of Kuipers and Veldman posted in Favaron and Fraisse (2001)[9], Lai
et al.(2006)[15] proved that if H is a 3-connected claw-free simple graph of order n≥ 196 …

For a graph H, let for every edge. For and, let be a set of k‐edge‐connected K3‐free graphs
of order at most r and without spanning closed trails. We show that for given and ε, if H is ak …

If G is a claw-free graph of sufficiently large order n, satisfying a degree condition σₖ> n+ k²-
4k+ 7 (where k is an arbitrary constant), then G has a 2-factor with at most k-1 components …

For a graph H, define σ̄2 (H)= min {d (u)+ d (v)| uvâE (H)}{{\bar\sigma}-2}(H)=\min\left\{{d
(u)+ d (v)| uv\in E (H)}\right\}. Let H be a 2-connected claw-free simple graph of order n with δ …

Spanning trails in a 2-connected graph Page 1 Spanning trails in a 2-connected graph
Shipeng Wang Liming Xiong School of Mathematics and Statistics Beijing Key Laboratory on …