Mathematics – Combinatorics
Scientific paper
2009-03-06
Diskretnyi Analiz, issue 31, 61--70, 91 (1977); Math. Rev. MR543806
Mathematics
Combinatorics
This is author's translation of his paper originally published in Russian
Scientific paper
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.
No associations
LandOfFree
On a certain representation of the chromatic polynomial does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On a certain representation of the chromatic polynomial, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a certain representation of the chromatic polynomial will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-135963