Document Type
Lecture
Publication Date
4-4-2012
Abstract
Let G be a graph on n vertices. If for any ordered set of vertices S = v1 v2 vk , that is, the vertices in S appear in order of the sequence v1 v2 vk, there exists a v1 vk (hamiltonian) path containing S in the given order, then G is k-ordered (hamiltonian) connected. Let u1 u2 and u3 u4 be any distinct pairs of nonadjacent vertices. We de ne 4 = mindG(u1) + dG(u2) + dG(u3) + dG(u4) when G= Kn and G= Kn e, otherwise set 4(G) = . In this talk we will present some new su cient conditions on the k-ordered connectivity based on 4. The main result is as follows: If 4(G) 2n+3k 10 (k 4), then G is k-ordered hamiltonian connected. Our outcomes generalize several related results known before.
Relational Format
presentation
Recommended Citation
Nicholson, Emlee, "Degree sum condition for k-ordered hamiltonian connected graphs" (2012). Combinatorics Seminar. 63.
https://egrove.olemiss.edu/math_combinatorics/63
