Short disjoint cycles in graphs with degree constraints

Minimum Degree and Disjoint Cycles in Claw-Free Graphs

Minimum degree and disjoint cycles in generalized claw-free graphs

For s ≥ 3 a graph is K1,s-free if it does not contain an induced subgraph isomorphic to K1,s. Cycles in K1,3-free graphs, called clawfree graphs, have beenwell studied. In this paper we extend results on disjoint cycles in claw-free graphs satisfying certain minimum degree conditions to K1,s-free graphs, normally called generalized claw-free graphs. In particular, we prove that if G is K1,s-fre...

Edge-disjoint Hamilton Cycles in Regular Graphs of Large Degree

Theorem 1 implies that if G is a A:-regular graph on n vertices and n ^ 2k, then G contains Wr(n + 3an + 2)] edge-disjoint Hamilton cycles. Thus we are able to increase the bound on the number of edge-disjoint Hamilton cycles by adding a regularity condition. In [5] Nash-Williams conjectured that if G satisfies the conditions of Theorem 2, then G contains [i(n + l)] edge-disjoint Hamilton cycle...

Disjoint Cycles and Chorded Cycles in Graphs

Very recently, Bialostocki et al. proposed the following conjecture. Let r, s be two nonnegative integers and let G = (V (G), E(G)) be a graph with |V (G)| ≥ 3r + 4s and minimum degree δ(G) ≥ 2r + 3s. Then G contains a collection of r cycles and s chorded cycles, all vertex-disjoint. We prove that this conjecture is true.

Disjoint Hamiltonian cycles in graphs

Let G be a 2(k + I)-connected graph of order n. It is proved that if uv rJ. E(G) implies that max{d(u), d(v)} ?: ~ + 2k then G contains k + 1 pairwise disjoint Hamiltonian cycles when c5 (G) ?: 4k + 3. 1 .. Introduction All graphs we consider are finite and simple. We use standard terminology and notation from Bondy and Murty [2] except as indicated. Let G = (V(G), E(G)) be a graph with vertex ...