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Hardness of approximation of graph partitioning into balanced complete bipartite subgraphs

Hardness of approximation of graph partitioning into balanced complete bipartite subgraphs
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Decompositions of complete graphs into isomorphic bipartite subgraphs

Graphs and Combinatorics, 1994
Let \(f\) be a 1-1 mapping of \(V(G)\) into the set \(S= \{0,1,\dots,| E(G)|\}\). Then \(f\) is called a \(\beta\)-valuation of \(G\) if the induced function \(\overline f: E(G)\to S\) given by \(\overline f(uv)= | f(u)- f(v)|\), for all \(uv\in E(G)\), is 1-1.
Balakrishnan, R., Sampath Kumar, R.
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On Vertex-Disjoint Complete Bipartite Subgraphs in a Bipartite Graph

Graphs and Combinatorics, 1999
It is proved that if \(G=(X,Y;E)\) is a bipartite graph with \(|X|=|Y|=4s\), \(s\geq 2\), and the minimum degree of \(G\) is at least \(4s-3\), then \(G\) contains four vertex-disjoint copies of \(K_{s,s}\).
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Complete bipartite graphs without small rainbow subgraphs

Discrete Applied Mathematics
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Zhiqiang Ma, Yaping Mao, Ingo Schiermeyer, Meiqin Wei   +3 more
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Bisections of directed graphs without complete bipartite subgraphs

Discrete Mathematics
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Wanjuan Ma, Shufei Wu
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Large Complete Bipartite Subgraphs In Incidence Graphs Of Points And Hyperplanes

SIAM Journal on Discrete Mathematics, 2007
We show that if the number $I$ of incidences between $m$ points and $n$ planes in $\mathbb{R}^3$ is sufficiently large, then the incidence graph (which connects points to their incident planes) contains a large complete bipartite subgraph involving $r$ points and $s$ planes, so that $rs \ge \frac{I^2}{mn} - a(m+n)$, for some constant $a>0$.
Roel Apfelbaum, Micha Sharir
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On the decomposition of graphs into complete bipartite subgraphs

1983
For a given graph G, we consider a B-decomposition of G, i. e., a decomposition of G into complete bipartite subgraphs G 1..., G t , such that any edge of G is in exactly one of the G′ i s. Let α(G; B) denote the minimum value of \(\sum\limits_i {|V(G_i )|}\) over all B-decompositions of G.
F. R. K. Chung, P. Erdős, J. Spencer
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Bipartite Complete Induced Subgraphs of a Random Graph

1985
Let G ( n, p ) denote a random graph on n labelled vertices in which the edges are chosen independently and with a fixed probability p . We study the number of vertices in the largest bipartite complete induced subgraph of a random graph G ( n, p ).
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Anti-Ramsey Problems in Complete Bipartite Graphs for t Edge-Disjoint Rainbow Spanning Subgraphs: Cycles and Matchings

Graphs and Combinatorics, 2019
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Jia, Yuxing, Lu, Mei, Zhang, Yi
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Covering of graphs by complete bipartite subgraphs; Complexity of 0–1 matrices

Combinatorica, 1984
The author proves that the edge set of an arbitrary graph G on n vertices can be covered by at most \(n-[\log_ 2n]+1\) complete bipartite subgraphs of G. This result improves the upper bound of J. C. Bermond. If the weight of a subgraph is the number of its vertices, then the author proves that there always exists a cover with total weight \(c(n^ 2 ...
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