## Abstract For integers __m, k__β₯1, we investigate the maximum size of a directed cut in directed graphs in which there are __m__ edges and each vertex has either indegree at most __k__ or outdegree at most __k__. Β© 2009 Wiley Periodicals, Inc. J Graph Theory
Maximum Directed Cuts in Graphs with Degree Constraints
β Scribed by Baogang Xu, Xingxing Yu
- Book ID
- 113036253
- Publisher
- Springer Japan
- Year
- 2011
- Tongue
- English
- Weight
- 310 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
## Abstract It is easily shown that every digraph with __m__ edges has a directed cut of size at least __m__/4, and that 1/4 cannot be replaced by any larger constant. We investigate the size of the largest directed cut in __acyclic__ digraphs, and prove a number of related results concerning cuts
Sheehan, J., Balanced graphs with minimum degree constraints, Discrete Mathematics 102 (1992) 307-314. Let G be a finite simple graph on n vertices with minimum degree 6 = 6(G) (n = 6 (mod 2)). Suppose that 0 < 6 c n -2, 06 i 4 [?Sl. A partition (x, Y) of V(G) is said to be an (i, a)-partition of G
Given a graph with n nodes and minimum degree 6, we give a polynomial time algorithm that constructs a partition of the nodes of the graph into two sets X and Y such that the sum of the minimum degrees in X and in Y is at least 6 and the cardinalities of X and Y differ by at most 6 (6 + 1 if n ~ 6 (