Improved approximation of max-cut on graphs of bounded degree
Journal of Algorithms
Problems and results on judicious partitions
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Bipartite subgraphs of triangle-free subcubic graphs
Journal of Combinatorial Theory Series B
Bipartite density of triangle-free subcubic graphs
Discrete Applied Mathematics
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A graph is subcubic if its maximum degree is at most 3. The bipartite density of a graph G is max{@e(H)/@e(G):H is a bipartite subgraph of G}, where @e(H) and @e(G) denote the numbers of edges in H and G, respectively. It is an NP-hard problem to determine the bipartite density of any given triangle-free cubic graph. Bondy and Locke gave a polynomial time algorithm which, given a triangle-free subcubic graph G, finds a bipartite subgraph of G with at least 45@e(G) edges; and showed that the Petersen graph and the dodecahedron are the only triangle-free cubic graphs with bipartite density 45. Bondy and Locke further conjectured that there are precisely seven triangle-free subcubic graphs with bipartite density 45. We prove this conjecture of Bondy and Locke. Our result will be used in a forthcoming paper to solve a problem of Bollobas and Scott related to judicious partitions.