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Hamiltonicity and restricted block-intersection graphs of -designs

✍ Scribed by David A. Pike; Robert C. Vandell; Matthew Walsh

Book ID
108114159
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
344 KB
Volume
309
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES

Hamilton cycles in block-intersection gr
Hamilton cycles in block-intersection graphs of triple systems
✍ Peter HorΓ‘k; David A. Pike; Michael E Raines πŸ“‚ Article πŸ“… 1999 πŸ› John Wiley and Sons 🌐 English βš– 336 KB πŸ‘ 3 views

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.

Existential closure of block intersectio
Existential closure of block intersection graphs of infinite designs having infinite block size
✍ Daniel Horsley; David A. Pike; Asiyeh Sanaei πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 143 KB

A graph G is n-existentially closed (n-e.c.) if for each pair (A,B) of disjoint subsets of V(G) with |A|+|B|≀n there exists a vertex in V(G)\(AβˆͺB) which is adjacent to each vertex in A and to no vertex in B. In this paper we study the n-existential closure property of block intersection graphs of in

Existential closure of block intersectio
Existential closure of block intersection graphs of infinite designs having finite block size and index
✍ David A. Pike; Asiyeh Sanaei πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 129 KB

In this article we study the n-existential closure property of the block intersection graphs of infinite t-(v, k, k) designs for which the block size k and the index k are both finite. We show that such block intersection graphs are 2-e.c. when 2 ≀ t ≀ k-1. When k = 1 and 2 ≀ t ≀ k, then a necessary