This is the first one in a series of two papers, in which we complete the characterization of
forbidden generalized nets implying Hamilton‐connectedness of a 3‐connected claw‐free …

Every 3-connected {K1,3,Z7}-free graph of order at least 21 is Hamilton-connected -
ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books Search …

In this paper, we show that if G is a 3‐edge‐connected graph with S⊆V(G) and |S|≤12, then
either G has an Eulerian subgraph H such that S⊆V(H), or G can be contracted to the …

The circumference of a graph is the length of its longest cycles. Jackson established a
conjecture of Bondy by showing that the circumference of a 3-connected cubic graph of …

A well-known result of Dirac (Math. Nachr. 22 (1960) 61) says that given n vertices in an n-
connected G, G has a cycle through all of them. In this paper, we generalize Dirac's result as …

Let H be a 3-connected claw-free graph on n vertices, and define σ 2 (H)= min {d H (u)+ d H
(v): uv∉ E (H)}. Kužel et al. proved that H is Hamilton-connected if n≥ 142 and δ (H)≥ n+ 50 …

Circuits through prescribed vertices in <i>k</i>â•’connected <i>k</i>â•’regular graphs Page 1
Circuits Through Prescribed Vertices in k-Connected k-Regular Graphs Roland HaÈggkvist and …

The cyclability of a graph H, denoted by C (H), is the largest integer r such that H has a cycle
through any r vertices. For a claw-free graph H, by Ryjáček (J Comb Theory Ser B 70: 217 …

A circuit in a simple undirected graph G=(V, E) is a sequence of vertices {v_1, v_2,..., v_ {k+
1}} such that v_1= v_ {k+ 1} and {v_i, v_ {i+ 1}}\in E for i= 1,..., k. A circuit C is said to be edge …