Learn More
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)
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)
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 Ryjᢠcek's line graph closure, it follows that every 3-connected, essentially 11-connected claw-free graph is(More)
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)
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)