Balanced cycles and holes in bipartite graphs
نویسندگان
چکیده
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 + 1 or I, l determine whether G contains a cycle whose weight is a multiple of 4, l determine whether G contains a chordless cycle whose weight is a multiple of 4. Given a bipartite graph, we can also decide whether it is possible to assign weights + I or 1 to its edges so that the above two properties hold. @ 1999 Elsevier Science B.V. All rights reserved
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عنوان ژورنال:
- Discrete Mathematics
دوره 199 شماره
صفحات -
تاریخ انتشار 1999