TY - JOUR
T1 - Cutting a graph into two dissimilar halves
AU - Erdós, Paul
AU - Goldberg, Mark
AU - Pach, János
AU - Spencer, Joel
PY - 1988
Y1 - 1988
N2 - Given a graph G and a subset S of the vertex set of G, the discrepancy of S is defined as the difference between the actual and expected numbers of the edges in the subgraph induced on S. We show that for every graph with n vertices and e edges, n < e < n(n − 1)/4, there is an n/2‐element subset with the discrepancy of the order of magnitude of \documentclass{article}\pagestyle{empty}\begin{document}$\sqrt {ne}$\end{document} For graphs with fewer than n edges, we calculate the asymptotics for the maximum guaranteed discrepancy of an n/2‐element subset. We also introduce a new notion called “bipartite discrepancy” and discuss related results and open problems.
AB - Given a graph G and a subset S of the vertex set of G, the discrepancy of S is defined as the difference between the actual and expected numbers of the edges in the subgraph induced on S. We show that for every graph with n vertices and e edges, n < e < n(n − 1)/4, there is an n/2‐element subset with the discrepancy of the order of magnitude of \documentclass{article}\pagestyle{empty}\begin{document}$\sqrt {ne}$\end{document} For graphs with fewer than n edges, we calculate the asymptotics for the maximum guaranteed discrepancy of an n/2‐element subset. We also introduce a new notion called “bipartite discrepancy” and discuss related results and open problems.
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U2 - 10.1002/jgt.3190120113
DO - 10.1002/jgt.3190120113
M3 - Article
AN - SCOPUS:84986529368
SN - 0364-9024
VL - 12
SP - 121
EP - 131
JO - Journal of Graph Theory
JF - Journal of Graph Theory
IS - 1
ER -