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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

1 vote
0 answers
70 views

Planar triangulations for which all distinct 4-colorings consist of exactly 6 Kempe chains

Are there any internally 6-connected planar triangulations other than the icosahedron all of whose distinct 4-colorings consist of exactly 6 Kempe chains, one for each of the 6 color-pairs? Addendum: …
Jim Tilley's user avatar
6 votes
0 answers
116 views

Chromatic numbers for coloring-constrained graphs

I am interested in any and all articles about chromatic numbers applying to constrained colorings of a graph. For example, if a graph must be (properly) colored so that there is a 2-color path betwee …
Jim Tilley's user avatar