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arXiv · 1705.02124

Terminal-Pairability in Complete Bipartite Graphs with Non-Bipartite Demands

Lucas Colucci·Péter L. Erdős·Ervin Győri·Tamás Róbert Mezei
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Abstract

We investigate the terminal-pairability problem in the case when the base graph is a complete bipartite graph, and the demand graph is a (not necessarily bipartite) multigraph on the same vertex set. In computer science, this problem is known as the edge-disjoint paths problem. We improve the lower bound on the maximum value of $\Delta(D)$ which still guarantees that the demand graph $D$ has a realization in $K_{n,n}$. We also solve the extremal problem on the number of edges, i.e., we determine the maximum number of edges which guarantees that a demand graph is realizable in $K_{n,n}$.

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Lucas Colucci, Péter L. Erdős, Ervin Győri, Tamás Róbert Mezei. 2017-05-05. Terminal-Pairability in Complete Bipartite Graphs with Non-Bipartite Demands. https://doi.org/10.1016/j.tcs.2018.12.007

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