Extremal results regarding $K_6$-minors in graphs of girth at least 5

Details Extremal results regarding $K_6$-minors in graphs of girth at least 5 Extremal results regarding $K_6$-minors in graphs of girth at least 5

2010-12-28

arxiv.org/abs/1012.5795v1

Mathematics

Combinatorics

13 pages, submitted on October 12 2010

Scientific paper

We prove that every 6-connected graph of girth $\geq 6$ has a $K_6$-minor and
thus settle the Jorgensen conjecture for graphs of girth $ \geq 6$. Relaxing
the assumption on the girth, we prove that every 6-connected $n$-vertex graph
of size $\geq 3 1/5 n-8$ and of girth $\geq 5$ contains a $K_6$-minor.

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