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- Hong-Jian Lai, Yehong Shao, Hehui Wu, Ju Zhou
- J. Comb. Theory, Ser. B
- 2009

It is shown that every (2p + 1) log 2 (|V (G)|)-edge-connected graph G has a mod (2p + 1)-orientation, and that a (4p + 1)-regular graph G has a mod (2p + 1)-orientation if and only if V (G) has a partition (V + , V −) such that ∀U ⊆ V (G), These extend former results by Da Silva and Dahad on nowhere zero 3-flows of 5-regular graphs, and by Lai and Zhang on… (More)

- HongJian Lai, Lianying Miao, Yehong Shao, Liangxia Wan
- 2004

A graph G is triangularly connected if for every pair of edges e 1 , e 2 ∈ E(G), G has a sequence of 3-cycles C 1 , C 2 , · · · , C l such that e 1 ∈ C 1 , e 2 ∈ C l and such that E(C i) ∩ E(C i+1) = ∅, (1 ≤ i ≤ l − 1). In this paper it is shown that every triangularly connected claw-free graph G with |E(G)| ≥ 3 is vertex pancyclic. This implies the former… (More)

- Paul A. Catlin, Hong-Jian Lai, Yehong Shao
- Discrete Mathematics
- 2009

Discrete Mathematics xx (xxxx) xxx–xxx

- Hong-Jian Lai, Yehong Shao, Gexin Yu, Mingquan Zhan
- Discrete Applied Mathematics
- 2009

We investigate graphs G such that the line graph L(G) is hamiltonian connected if and only if L(G) is 3-connected, and prove that if each 3-edge-cut contains an edge lying in a short cycle of G, then L(G) has the above mentioned property. Our result extends Kriesell's recent result in [

- Hong-Jian Lai, Yehong Shao, Mingquan Zhan
- Journal of Graph Theory
- 2005

A graph G is N 2-locally connected if for every vertex v in G, the edges not incident with v but having at least one end adjacent to v in G induce a connected graph. In 1990, Ryjá˘ cek conjectured that every 3-connected N 2-locally connected claw-free graph is hamiltonian. This conjecture is proved in this note.

- Hong-Jian Lai, Yehong Shao, Hehui Wu, Ju Zhou
- J. Comb. Theory, Ser. B
- 2006

Thomassen conjectured that every 4-connected line graph is Hamiltonian. A vertex cut X of G is essential if G − X has at least two non-trivial components. We prove that every 3-connected, essentially 11-connected line graph is Hamiltonian. Using Ryjá˘ cek's line graph closure, it follows that every 3-connected, essentially 11-connected claw-free graph is… (More)

- Suohai Fan, Hong-Jian Lai, Yehong Shao, Taoye Zhang, Ju Zhou
- Discrete Mathematics
- 2008

A sequence d = (d 1 , d 2 , · · · , d n) is graphic if there is a simple graph G with degree sequence d, and such a graph G is called a realization of d. A graphic sequence d is line-hamiltonian if d has a realization G such that L(G) is hamiltonian, and is supereulerian if d has a realization G with a spanning eulerian subgraph. In this paper, it is proved… (More)

In 1950s, Tutte introduced the theory of nowhere-zero flows as a tool to investigate the coloring problem of maps, together with his most fascinating conjectures on nowhere-zero flows. These have been extended by Jaeger et al. in 1992 to group connectivity, the nonhomogeneous form of nowhere-zero flows. Let G be a 2-edge-connected undirected graph, A be an… (More)

- Hong-Jian Lai, Yehong Shao, Mingquan Zhan
- Discrete Mathematics
- 2008

Let G be a graph. For u, v ∈ V (G) with distG(u, v) = 2, denote JG(u, v) = {w ∈ NG(u) ∩ NG(v)|NG(w) ⊆ NG(u) ∪ NG(v) ∪ {u, v}}. A graph G is called quasi claw-free if JG(u, v) = ∅ for any u, v ∈ V (G) with distG(u, v) = 2. In 1986, Thomassen conjectured that every 4-connected line graph is hamiltonian. In this paper we show that every 4-connected line graph… (More)

We prove that every line graph of a 4-edge-connected graph is Z 3-connected. In particular, every line graph of a 4-edge-connected graph has a nowhere zero 3-flow.