Add to ORKGIn this article, we consider Vizing\u27s 2-Factor Conjecture which claims that any Δ-critical graph has a 2-factor, and show that if G is a Δ-critical graph with n vertices satisfying Δ≥6n/7, then G is Hamiltonian and thus G has a 2-factor. Meanwhile in this article, we also consider long cycles of overfull critical graphs and obtain that if G is an overfull Δ-critical graph with n vertices, then the circumference of G is at least min{2Δ,n}.© 2012 Wiley Periodicals, Inc. J. Graph Theory 00: 1-14, 2012 © 2012 Wiley Periodicals, Inc
AbstractA graph G is said to be n-factor-critical if G−T has a perfect matching for each T⊂V(G) with...
A graph G=(V, E) is called a complete semi-bigraph and denoted by K'(l, m) if the vertex set can be ...
DeLeon 1 A graph G is Hamiltonian if it has a spanning cycle. The problem of determining if a graph ...
In this article, we consider Vizing\u27s 2-Factor Conjecture which claims that any -critical graph h...
Abstract. Let G be a simple graph of order n, and let ∆(G) and ′(G) denote the maximum degree and ch...
AbstractA graph G is said to be n-factor-critical if G−S has a 1-factor for any S⊂V(G) with |S|=n. I...
It is shown by Luo and Zhao (J Graph Theory 73:469–482, 2013) that an overfull Δ -critical graph wit...
A well known generalisation of Dirac's theorem states that if a graph G on n≥4k vertices has minimum...
AbstractIn this paper we generalize a Theorem of Jung which shows that 1-tough graphs with δ(G)⩾|V(G...
We show that every hamiltonian claw-free graph with a ver-tex x of degree d(x) ≥ 7 has a 2-factor c...
Let a and b be nonnegative integers with 2 ≤ a < b, and let G be a Hamiltonian graph of order n with...
Let G be a 2-connected graph of order n satisfying α(G) = a ≤ κ(G), where α(G) and κ(G) are the inde...
AbstractIn this paper we study the minimum degree condition for a Hamiltonian graph to have a 2-fact...
AbstractA new sufficient condition for a graph to be Hamiltonian is given that does not require that...
Let G be a Hamiltonian graph. A factor F of G is called a Hamiltonian factor if F contains a Hamilto...
AbstractA graph G is said to be n-factor-critical if G−T has a perfect matching for each T⊂V(G) with...
A graph G=(V, E) is called a complete semi-bigraph and denoted by K'(l, m) if the vertex set can be ...
DeLeon 1 A graph G is Hamiltonian if it has a spanning cycle. The problem of determining if a graph ...
In this article, we consider Vizing\u27s 2-Factor Conjecture which claims that any -critical graph h...
Abstract. Let G be a simple graph of order n, and let ∆(G) and ′(G) denote the maximum degree and ch...
AbstractA graph G is said to be n-factor-critical if G−S has a 1-factor for any S⊂V(G) with |S|=n. I...
It is shown by Luo and Zhao (J Graph Theory 73:469–482, 2013) that an overfull Δ -critical graph wit...
A well known generalisation of Dirac's theorem states that if a graph G on n≥4k vertices has minimum...
AbstractIn this paper we generalize a Theorem of Jung which shows that 1-tough graphs with δ(G)⩾|V(G...
We show that every hamiltonian claw-free graph with a ver-tex x of degree d(x) ≥ 7 has a 2-factor c...
Let a and b be nonnegative integers with 2 ≤ a < b, and let G be a Hamiltonian graph of order n with...
Let G be a 2-connected graph of order n satisfying α(G) = a ≤ κ(G), where α(G) and κ(G) are the inde...
AbstractIn this paper we study the minimum degree condition for a Hamiltonian graph to have a 2-fact...
AbstractA new sufficient condition for a graph to be Hamiltonian is given that does not require that...
Let G be a Hamiltonian graph. A factor F of G is called a Hamiltonian factor if F contains a Hamilto...
AbstractA graph G is said to be n-factor-critical if G−T has a perfect matching for each T⊂V(G) with...
A graph G=(V, E) is called a complete semi-bigraph and denoted by K'(l, m) if the vertex set can be ...
DeLeon 1 A graph G is Hamiltonian if it has a spanning cycle. The problem of determining if a graph ...