MATH Seminar

Title: Minimum Degree and Disjoint Cycles in Generalized Claw-free Graphs
Seminar: Combinatorics
Speaker: Ralph Faudree of The University of Memphis
Contact: Dwight Duffus, dwight@math.cs.emory.edu
Date: 2012-09-14 at 4:00PM
Venue: MSC W303
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Abstract: For $s \geq 3$ a graph is $K_{1,s}$-free, if it does not contain an induced subgraph isomorphic to $K_{1,s}$. For $s = 3$, such graphs are called claw-free graphs. Results on disjoint cycles in claw-free graphs satisfying certain minimum degree conditions will be be discussed, such as if $G$ is claw-free of sufficiently large order $n = 3k$ with $\delta (G) \geq n/2$, then $G$ contains $k$ disjoint triangles. Also, the extension of results on disjoint cycles in claw-free graphs satisfying certain minimum degree conditions to $K_{1,s}$-free graphs for $s > 3$ will be presented. These results will be used to prove the existence of minimum degree conditions that imply the existence of powers Hamiltonian cycle in generalized claw-free graphs.