Bruce Reed asks the following question: Can we determine whether a bipartite graph contains a chordless cycle whose length is a multiple of 4? We show that the two following more general questions are equivalent and we provide an answer. Given a bipartite graph G where each edge is assigned a weight
Cycles in bipartite graphs and an application in number theory
✍ Scribed by Gábor N. Sárközy
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 304 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Let G = G(A, B) be a bipartite graph with IAl = u, IBl = U , and let I be a positive integer. In this paper we prove the following result: If u 4 u, uu 5 n, rn = J€(G)I, and
then G contains a C2/.
📜 SIMILAR VOLUMES
In this paper we obtain two sufficient conditions, Ore type (Theorem 1) and Dirac type (Theorem 2). on the degrees of a bipartite oriented graph for ensuring the existence of long paths and cycles. These conditions are shown to be the best possible in a sense. An oriented graph is a digraph without
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## Abstract We give necessary and sufficient conditions for the existence of an alternating Hamiltonian cycle in a complete bipartite graph whose edge set is colored with two colors.