Bipartite Subgraphs of Triangle-Free Graphs
SIAM Journal on Discrete Mathematics
Bipartite subgraphs of integer weighted graphs
Discrete Mathematics
Polarities and 2k-cycle-free graphs
Discrete Mathematics
Norm-graphs: variations and applications
Journal of Combinatorial Theory Series B
On the spectrum of projective norm-graphs
Information Processing Letters
Maximum cuts and judicious partitions in graphs without short cycles
Journal of Combinatorial Theory Series B
Turán Numbers of Bipartite Graphs and Related Ramsey-Type Questions
Combinatorics, Probability and Computing
Sharp Bounds For Some Multicolor Ramsey Numbers
Combinatorica
Edge Distribution of Graphs with Few Copies of a Given Graph
Combinatorics, Probability and Computing
Algorithms for the Minimum Edge Cover of H-Subgraphs of a Graph
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Modular orientations of random and quasi-random regular graphs
Combinatorics, Probability and Computing
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For a graph G, let f(G) denote the maximum number of edges in a cut of G. For an integer m and for a fixed graph H, let $f(m,H)$ denote the minimum possible cardinality of $f(G)$, as G ranges over all graphs on m edges that contain no copy of H. In this paper we study this function for various graphs H. In particular we show that for any graph H obtained by connecting a single vertex to all vertices of a fixed nontrivial forest, there is a $c(H) 0$ such that $f(m,H) \geq \frac{m}{2} + c(H) m^{4/5}$, and that this is tight up to the value of $c(H)$. We also prove that for any even cycle $C_{2k}$ there is a $c(k)0$ such that $f(m,C_{2k}) \geq \frac{m}{2} + c(k) m^{(2k+1)/(2k+2)}$, and that this is tight, up to the value of $c(k)$, for $2k\in \{4,6,10\}$. The proofs combine combinatorial, probabilistic and spectral techniques.