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- W2120650079 abstract "We investigate the maximum number of edges that a graph G can have if it does not contain a given graph H as a minor (subcontraction). Let $$ c{left( H right)} = inf {left{ {c:e{left( G right)} geqslant c{left| G right|}{text{implies}}{kern 1pt} {kern 1pt} G succ H} right}}. $$ We define a parameter γ(H) of the graph H and show that, if H has t vertices, then $$ c{left( H right)} = {left( {alpha gamma {left( H right)} + o{left( 1 right)}} right)}t{sqrt {log {kern 1pt} {kern 1pt} t} } $$ where α = 0.319. . . is an explicit constant and o(1) denotes a term tending to zero as t→∞. The extremal graphs are unions of pseudo-random graphs. If H has t1+τ edges then $$ gamma {left( H right)} leqslant {sqrt tau } $$ , equality holding for almost all H and for all regular H. We show how γ(H) might be evaluated for other graphs H also, such as complete multi-partite graphs." @default.
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- W2120650079 date "2005-12-01" @default.
- W2120650079 modified "2023-10-04" @default.
- W2120650079 title "The Extremal Function For Noncomplete Minors" @default.
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- W2120650079 doi "https://doi.org/10.1007/s00493-005-0044-0" @default.
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