We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Minimum Degree Conditions for Cycles Including Specified Sets of Vertices.
- Authors
Goddard, Wayne
- Abstract
This paper generalises the concept of vertex pancyclic graphs. We define a graph as set-pancyclic if for every setSof vertices there is a cycle of every possible length containingS. We show that if the minimum degree of a graph exceeds half its order then the graph is set-pancyclic. We define a graph ask-ordered-pancyclic if, for every setSof cardinalitykand every cyclic ordering ofS, there is for every possible length a cycle of that length containingSand encounteringSin the specified order. We determine the best possible minimum-degree condition which guarantees that a graph isk-ordered-pancyclic.
- Subjects
GRAPH theory; ALGEBRA; COMBINATORICS; TOPOLOGY; SET theory; MATHEMATICS
- Publication
Graphs & Combinatorics, 2004, Vol 20, Issue 4, p467
- ISSN
0911-0119
- Publication type
Article
- DOI
10.1007/s00373-004-0565-0