Apr 13, 2011 · We develop lower bounds on the Hadwiger number h(G) of graphs G with high chromatic number. In particular, if G has n vertices and chromatic ...
Apr 13, 2011 · Introduction. The order of the largest complete minor of a graph G is called the Hadwiger number of G, denoted by h(G).
We develop lower bounds on the Hadwiger number h(G) of graphs G with high chromatic number. In particular, if G has n vertices and chromatic number k then ...
Oct 22, 2024 · The order of the largest complete minor of a graph G is called the Hadwiger number of G, denoted by h(G). The well-known conjecture of ...
Jun 30, 2021 · Upper bounding the chromatic number of a graph minor ... Let H be a minor of G. By letting G be an even cycle, we see that χ(H)≤χ(G) does not hold ...
Jul 4, 2017 · Minors of graphs with infinite chromatic number ... Let e be an edge of G and let M=G−e. Doesn't this already work? Clearly M is a minor of G and ...
Apr 13, 2011 · Introduction. The order of the largest complete minor of a graph G is called the Hadwiger number of G, denoted by h(G).
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Jan 6, 2018 · There are two non-adjacent vertices v,w∈V such that when v and w are identified, the Hadwiger number of the resulting graph is smaller than h(G) ...
Since the infimum in the definition of XC(G ) can be replaced by minimum for finite graphs, we know that XC(G) is a rational number for any finite graph G.
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... graphs that is closed under minors, there is a finite set M of graphs such that a graph G is in G if and only if it does not contain any graph in M as a minor.