On a certain representation of the chromatic polynomial
| dc.creator | Matiyasevich, Yu. V. | |
| dc.date | 2009-03-06 | |
| dc.date.accessioned | 2026-07-07T12:49:53Z | |
| dc.date.available | 2026-07-07T12:49:53Z | |
| dc.description | The representation is essentially the same as that given by J.P.Nagle in J. Comb. Theory (B), 1971, 10:1, 42--59. The distinction is in the definition of the weighting function via the number of flows. This new definition allows one to deduce a number of corollaries, in particular, the following. A) The chromatic polynomial of a connected planar graph G can be uniquely determined from its combinatory dual graph G^* (although the graph G itself isn't, in general, determined uniquely by G^*). B) If a planar graph G is different from the full graph K_3 and has exactly one (up to renaming of colors) proper coloring of vertices in three colors, then the graph G^* dual to graph G is also vertex colorable in three colors. | |
| dc.description | This is author's translation of his paper originally published in Russian | |
| dc.identifier | https://arxiv.org/abs/0903.1213 | |
| dc.identifier | http://arxiv.org/abs/0903.1213 | |
| dc.identifier | Diskretnyi Analiz, issue 31, 61--70, 91 (1977); Math. Rev. MR543806 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222524 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C15 | |
| dc.title | On a certain representation of the chromatic polynomial | |
| dc.type | text |