## 24 Citations

Disproof of a Conjecture by Woodall

- Mathematics
- 2022

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…

Forcing a sparse minor

- MathematicsCombinatorics, Probability and Computing
- 2015

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$ .

Linear connectivity forces large complete bipartite minors

- MathematicsJ. Comb. Theory, Ser. B
- 2009

On Ks, t-minors in graphs with given average degree, II

- MathematicsDiscret. Math.
- 2012

Average Degree Conditions Forcing a Minor

- MathematicsElectron. J. Comb.
- 2016

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

- MathematicsSIAM J. Discret. Math.
- 2015

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 $k \geq 6$.

## References

SHOWING 1-10 OF 16 REFERENCES

Graphs without Large Complete Minors are Quasi-Random

- MathematicsCombinatorics, Probability and Computing
- 2002

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.

The Extremal Function for Complete Minors

- MathematicsJ. Comb. Theory, Ser. B
- 2001

Let c(t) be the minimum number c such that every graph G with e(G)?c|G| contracts to a complete graph Kt where ?=0.319... is an explicit constant.

Lower bound of the hadwiger number of graphs by their average degree

- MathematicsComb.
- 1984

The aim of this paper is to show that the minimum Hadwiger number of graphs with average degreek isO(k/√logk). Specially, it follows that Hadwiger’s conjecture is true for almost all graphs withn…

Highly linked graphs

- MathematicsComb.
- 1996

It is shown here that k (G)≥22k will do and that a graphG isk-linked provided its vertex connectivityk(G) exceeds 10k\sqrt {\log _2 k}$$ .

An extremal function for contractions of graphs

- Mathematics
- 1984

The function c ( p ) is defined for positive integers p ≥ 4 by where > denotes contraction. Random graph examples show In 1968 Mader showed that c ( p ) ≤ 8( p − 2) [log 2 ( p − 2)] and more recently…

On Sufficient Degree Conditions for a Graph to be $k$-linked

- MathematicsCombinatorics, Probability and Computing
- 2006

The bound allows the Thomas–Wollan proof slightly to be modified slightly to show that every $2k-connected graph with average degree at least $12k$ is $k$-linked.

The Extremal Function For Noncomplete Minors

- MathematicsComb.
- 2005

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.