Hadwiger's conjecture for proper circular arc graphs
نویسندگان
چکیده
Circular arc graphs are graphs whose vertices can be represented as arcs on a circle such that any two vertices are adjacent if and only if their corresponding arcs intersect. Proper circular arc graphs are graphs which have a circular arc representation where no arc is completely contained in any other arc. Hadwiger’s conjecture states that if a graph G has chromatic number k, then a complete graph on k vertices is a minor of G. We prove Hadwiger’s conjecture for proper circular arc graphs.
منابع مشابه
Hadwiger’s conjecture on special classes of graphs
The Hadwiger number of a graph G is the largest integer n for which the complete graph on n vertices is a minor of G. Hadwiger conjectured that for any graph G, ,where is the chromatic number of G. We will address Hadwiger’s conjecture for circular arc graphs and their subfamilies. Circular arc graphs are graphs whose vertices can be represented as arcs on a circle such that any two vertices ar...
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عنوان ژورنال:
- Eur. J. Comb.
دوره 30 شماره
صفحات -
تاریخ انتشار 2009