Graph Characteristics and Hadwiger's Conjecture

Details Graph Characteristics and Hadwiger's Conjecture Graph Characteristics and Hadwiger's Conjecture

2012-03-16

arxiv.org/abs/1203.3710v3

Mathematics

Combinatorics

31 pages, 9 figures. The proof of Proposition 4.2.1 has been revised

Scientific paper

A graph charactristic $\beth$ is defined to be the function which assigns a number for each simple graph $G$ that decreases under arbitrary edge contractions and certain graph homomorphisms which are strong enough to yield a complete graph when applied to any given graph. Such function gives rise to a similtaneous upperbound for the hadwiger number $h(G)$ and the chromaric number $\chi(G)$, and when $h(G)$ equals the upper bound, the Hadwiger's conjecture is true. In this paper we study three different graph graph characteristics which are graph theoretical analog of the Euler characteristic, and discuss their implications and applications to Hadwiger's conjecture.

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