Given a BIBD S = (V, B), its 1-block-intersection graph GS has as vertices the elements of B; two vertices B1, B2 β B are adjacent in GS if |B1 β© B2| = 1. If S is a triple system of arbitrary index Ξ», it is shown that GS is hamiltonian.
Cycles in the block-intersection graph of pairwise balanced designs
β Scribed by Donovan R. Hare
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 580 KB
- Volume
- 137
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
It is shown that the block-intersection graph of a pairwise balance design with ),= l is edge-pancyclic given that its minimum block cardinality is at least 3.
π SIMILAR VOLUMES
Tian, F. and W. Zang, The maximum number of diagonals of a cycle in a block and its extremal graphs, Discrete Mathematics 89 (1991) 51-63. In this paper we show that if G is a 2-connected graph having minimum degree n such that IV(G)1 L 2n + 1, then there exists a cycle in G having more than n(n -2
## Abstract Kreher and Rees 3 proved that if __h__ is the size of a hole in an incomplete balanced design of order Ο and index Ξ» having minimum block size $k \ge t+1$, then, They showed that when __t__β=β2 or 3, this bound is sharp infinitely often in that for each __h__ββ₯β__t__ and each __k__ββ₯β_