Distance graphs having large chromatic numbers and not containing cliques or cycles of given size
| Autor: | Demekhin, Evgeniy, Raigorodskii, Andrei, Rubanov, Oleg |
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| Jazyk: | ruština |
| Rok vydání: | 2012 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1070/SM2013v204n04ABEH004310 |
| Popis: | In this work, the classical Nelson -- Hadwiger problem is studied which lies on the edge of combinatorial geometry and graph theory. It concerns colorings of distance graphs in $ {\mathbb R}^n $, i.e., graphs such that their vertices are vectors and their edges are pairs of vectors at a distance from a given set of postive numbers apart. A series of new lower bounds are obtained for the chromatic numbers of such graphs with different restrictions on the clique numbers and the girths. Comment: In Russian |
| Databáze: | arXiv |
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