par Cames Van Batenburg, Wouter 
;KANG, ROSS J.
Référence Combinatorics, probability & computing, 27, 5, page (725-740)
Publication Publié, 2018-09-01
;KANG, ROSS J.Référence Combinatorics, probability & computing, 27, 5, page (725-740)
Publication Publié, 2018-09-01
Article révisé par les pairs
| Résumé : | Two graphs G 1 and G 2 on n vertices are said to pack if there exist injective mappings of their vertex sets into [ n ] such that the images of their edge sets are disjoint. A longstanding conjecture due to Bollobás and Eldridge and, independently, Catlin, asserts that if (Δ( G 1 ) + 1)(Δ( G 2 ) + 1) ⩽ n + 1, then G 1 and G 2 pack. We consider the validity of this assertion under the additional assumption that G 1 or G 2 has bounded codegree. In particular, we prove for all t ⩾ 2 that if G 1 contains no copy of the complete bipartite graph K 2, t and Δ( G 1 ) > 17 t · Δ( G 2 ), then (Δ( G 1 ) + 1)(Δ( G 2 ) + 1) ⩽ n + 1 implies that G 1 and G 2 pack. We also provide a mild improvement if moreover G 2 contains no copy of the complete tripartite graph K 1,1, s , s ⩾ 1. |
