Forcing unbalanced complete bipartite minors

@article{Khn2005ForcingUC,
  title={Forcing unbalanced complete bipartite minors},
  author={Daniela K{\"u}hn and Deryk Osthus},
  journal={Eur. J. Comb.},
  year={2005},
  volume={26},
  pages={75-81}
}
Disproof of a Conjecture by Woodall
In 2001, in a survey article [26] about list coloring, Woodall conjectured that for every pair of integers s, t ≥ 1, all graphs without a Ks,t-minor are (s + t − 1)-choosable. In this note we refute
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  • B. Reed, D. Wood
  • Mathematics
    Combinatorics, Probability and Computing
  • 2015
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The main result, which complements the result of Myers and Thomason, states that if H has t vertices and average degree d at least some absolute constant, then f(H) ≤ 3.895\sqrt{\ln d}\,t$ .
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Disjoint complete minors and bipartite minors
Average Degree Conditions Forcing a Minor
TLDR
This work strengthens (under certain conditions) a recent result by Reed and Wood, giving better bounds on the average degree required to force an arbitrary graph as a minor when $H$ is a sparse graph with many high degree vertices.
Cycles of Given Size in a Dense Graph
TLDR
It is shown that every graph with average degree at least $\frac{4}{3}kr$ contains $k$ vertex disjoint cycles, each of order at least $r$ as long as $k \geq 6$.
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    Combinatorics, Probability and Computing
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TLDR
It is shown that, if a graph G of order n and density p has no complete minor larger than would be found in a random graph G(n, p), then G is quasi-random, provided either p > 0.45631 … or κ(G) [ges ] n( log log log n)/(log log n), where 0.45731 … is an explicit constant.
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TLDR
The maximum number of edges that a graph G can have if it does not contain a given graph H as a minor (subcontraction) is investigated and a parameter γ(H) of the graph H is defined, equality holding for almost all H and for all regular H.
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