Generalizations of critical connectivity of graphs
Discrete Mathematics - First Japan Conference on Graph Theory and Applications
Every planar graph is 5-choosable
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Choosability of K5-minor-free graphs
Discrete Mathematics
The extremal function for complete minors
Journal of Combinatorial Theory Series B
Triangle Density and Contractibility
Combinatorics, Probability and Computing
A relaxed Hadwiger's Conjecture for list colorings
Journal of Combinatorial Theory Series B
A weakening of the odd hadwiger's conjecture
Combinatorics, Probability and Computing
Linear connectivity forces large complete bipartite minors
Journal of Combinatorial Theory Series B
Thomassen's Choosability Argument Revisited
SIAM Journal on Discrete Mathematics
| Hi-index | 0.02 |
Consider the following relaxation of the Hadwiger Conjecture: For each t there exists N"t such that every graph with no K"t-minor admits a vertex partition into @?@at+@b@? parts, such that each component of the subgraph induced by each part has at most N"t vertices. The Hadwiger Conjecture corresponds to the case @a=1, @b=-1 and N"t=1. Kawarabayashi and Mohar [K. Kawarabayashi, B. Mohar, A relaxed Hadwiger's conjecture for list colorings, J. Combin. Theory Ser. B 97 (4) (2007) 647-651. URL: http://dx.doi.org/10.1016/j.jctb.2006.11.002] proved this relaxation with @a=312 and @b=0 (and N"t a huge function of t). This paper proves this relaxation with @a=72 and @b=-32. The main ingredients in the proof are: (1) a list colouring argument due to Kawarabayashi and Mohar, (2) a recent result of Norine and Thomas that says that every sufficiently large (t+1)-connected graph contains a K"t-minor, and (3) a new sufficient condition for a graph to have a set of edges whose contraction increases the connectivity.