Odd K3,3 subdivisions in bipartite graphs
Copyright policy )Odd K3,3 subdivisions in bipartite graphs
We prove that every internally 4-connected non-planar bipartite graph has an odd K_3,3 subdivision; that is, a subgraph obtained from K_3,3 by replacing its edges by internally disjoint odd paths with the same ends. The proof gives rise to a polynomial-time algorithm to find such a subdivision. (A bipartite graph G is internally 4-connected if it is 3-connected, has at least five vertices, and there is no partition (A,B,C) of V(G) such that |A|,|B|>1, |C|=3 and G has no edge with one end in A and the other in B.)
12 pages, 1 figure
- Georgia Institute of Technology United States
- GEORGIA TECH RESEARCH CORPORATION United States
FOS: Computer and information sciences, Connectivity, Discrete Mathematics (cs.DM), Pfaffian orientation, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), odd \(K_{3, 3}\) subdivision, bipartite graph, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Computer Science - Discrete Mathematics
FOS: Computer and information sciences, Connectivity, Discrete Mathematics (cs.DM), Pfaffian orientation, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), odd \(K_{3, 3}\) subdivision, bipartite graph, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Computer Science - Discrete Mathematics
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