Abstract
In a complete bipartite decomposition π of a graph, we consider the number ϑ(v;π) of complete bipartite subgraphs incident with a vertex v. Let ϑ(G)=\(\min \limits_{\pi } \max \limits_{v\in V(G)}\) ϑ(v;π). In this paper the exact values of ϑ(G) for complete graphs and hypercubes and a sharp upper bound on ϑ(G) for planar graphs are provided, respectively. An open problem proposed by P.C. Fishburn and P.L. Hammer is solved as well.
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Dong, J., Liu, Y. On the Decomposition of Graphs into Complete Bipartite Graphs. Graphs and Combinatorics 23, 255–262 (2007). https://doi.org/10.1007/s00373-007-0722-3
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DOI: https://doi.org/10.1007/s00373-007-0722-3