Let G be an r-regular graph of order n and independence number Î±(G). We show that if G has odd girth 2k + 3 then Î±(G) â‰¥ n1âˆ’1/kr1/k . We also prove similar results for graphs which are not regular.â€¦ (More)

The Evans conjecture states that an n Ã— n partial Latin square with at most nâˆ’ 1 entries is completable. We show that the condition of at most nâˆ’ 1 entries appearing is sufficient for completing nÃ—nâ€¦ (More)

A question of ErdÅ‘s asks if every graph with minimum degree 3 must contain a pair of cycles whose lengths di1er by 1 or 2. Some recent work of H3 aggkvist and Scott (see Arithmetic progressions ofâ€¦ (More)

In this paper, we combine the notions of completing and avoiding partial latin squares. Let P be a partial latin square of order n and let Q be the set of partial latin squares of order n that avoidâ€¦ (More)