Lech Adamus

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We prove a sharp Meyniel-type criterion for hamiltonicity of a balanced bipartite digraph: For a ≥ 2, a strongly connected balanced bipartite digraph D on 2a vertices is hamiltonian if d(u) + d(v) ≥ 3a whenever uv / ∈ A(D) and vu / ∈ A(D). As a consequence, we obtain a sharp sufficient condition for hamiltonicity in terms of the minimal degree: a strongly(More)
  • Lech Adamus
  • Electronic Notes in Discrete Mathematics
  • 2006
Consider the following problem (solved by Woodall): given p > |G| 2 , find the minimum size of a graph G guaranteeing the existence of a cycle of length p. We prove that a balanced bipartite graph of order 2n and size greater than n(n− k − 1) + k + 1 contains a cycle of length 2n− 2k, where n ≥ 12k + 32k + 4. In the paper we also formulate and give a(More)
  • Lech Adamus
  • Discrete Mathematics & Theoretical Computer…
  • 2009
The following problem was solved by Woodall in 1972: for any pair of nonnegative integers n and k < n2 find the minimum integer g(n, k) such that every graph with n vertices and at least g(n, k) edges contains a cycle of length n − k. Woodall proved even more: the size g(n, k), in fact, guarantees the existence of cycles Cp for all 3 ≤ p ≤ n− k. In the(More)
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