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URL:/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-daniel-horsley
SUMMARY:Algebraic Graph Theory - Daniel Horsley 
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE: Exact Zarankiewicz numbers through linear h
 ypergraphs\n\nSpeaker:\n Daniel Horsley \n\nAffiliation:\n Monash Universi
 ty\n\nLocation:\n Contact Sabrina Lato for Zoom link\n\nABSTRACT: The \\e
 mph{Zarankiewicz number} $Z_{2\,2}(m\,n)$ is usually\ndefined as the maxim
 um number of edges in a bipartite graph with parts\nof sizes $m$ and $n$ t
 hat has no $K_{2\,2}$ subgraph. An equivalent\ndefinition is that $Z_{2\,2
 }(m\,n)$ is the greatest total degree of a\nlinear hypergraph with $m$ ver
 tices and $n$ edges. A hypergraph is\n\\emph{linear} if each pair of verti
 ces appear together in at most one\nedge. The equivalence of the two defin
 itions can be seen by\nconsidering the bipartite incidence graph of the li
 near hypergraph.\n 
DTSTAMP:20250524T032950Z
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