It is well-known that the largest cycles of a graph may have empty intersection. This is the case, for example, for any hypohamiltonian graph. In the literature, several important classes of graphs have been shown to contain examples with the above property. This paper investigates a (nontrivial) cl
Hamilton cycles in block-intersection graphs of triple systems
✍ Scribed by Peter Horák; David A. Pike; Michael E Raines
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 336 KB
- Volume
- 7
- Category
- Article
- ISSN
- 1063-8539
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✦ Synopsis
Given a BIBD S = (V, B), its 1-block-intersection graph GS has as vertices the elements of B; two vertices B1, B2 ∈ B are adjacent in GS if |B1 ∩ B2| = 1. If S is a triple system of arbitrary index λ, it is shown that GS is hamiltonian.
📜 SIMILAR VOLUMES
We are interested in the sizes of cliques that are to be found in any arbitrary spanning graph of a Steiner triple system S S. In this paper we investigate spanning graphs of projective Steiner triple systems, proving, not surprisingly, that for any positive integer k and any suf®ciently large proje
Let G n,m,k denote the space of simple graphs with n vertices, m edges, and minimum degree at least k, each graph G being equiprobable. Let G have property A k , if G contains (k -1)/2 edge disjoint Hamilton cycles, and, if k is even, a further edge disjoint matching of size n/2 . We prove that, for