May 6, 2010 · A fundamental result in structural graph theory states that every graph with large average degree contains a large complete graph as a minor.
A fundamental result in structural graph theory states that every graph with large average degree contains a large complete graph as a minor.
What if our 'dense component' contains the root? each non-root vertex has degree ⩽ 2 in component. ⇒ avg degree ⩽ 4 < 2t−1 + ε ...
A fundamental result in structural graph theory states that every graph with large average degree contains a large complete graph as a minor.
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Mar 6, 2012 · We prove this result with the extra property that the minor is small with respect to the order of the whole graph. More precisely, we describe ...
For every integer t there is a smallest real number c ( t ) such that any graph with average degree at least c ( t ) must contain a K t -minor (proved by ...
Oct 22, 2024 · A fundamental result in structural graph theory states that every graph with large average degree contains a large complete graph as a minor ...
Original language, English. Pages (from-to), 1226 - 1245. Number of pages, 20. Journal, European Journal of Combinatorics. Volume, 33. Issue number, 6.
Our main result, stated below, guarantees in such graphs the existence of a minor with d|V (G)|/2e vertices and with fewer than 1/76 of all possible edges ...
Theorem 3.1 gives an asymptotically optimal criterion for general graphs containing a dense minor. Here is a related result (cf. [16, Lemma 3.1]) with a ...