21 research outputs found
Realizing the chromatic numbers and orders of spinal quadrangulations of surfaces
A method is suggested for construction of quadrangulations of the closed
orientable surface with given genus g and either (1) with given chromatic
number or (2) with given order allowed by the genus g. In particular, N.
Hartsfield and G. Ringel's results [Minimal quadrangulations of orientable
surfaces, J. Combin. Theory, Series B 46 (1989) 84-95] are generalized by way
of generating new minimal quadrangulations of infinitely many other genera.Comment: 6 pages. This version is only slightly different from the original
version submitted on 8 Jul 2012: the author's affiliation has been changed
and the presentation has been slightly improve
Realizing the chromatic numbers of triangulations of surfaces
AbstractGiven an orientable or nonorientable closed surface S and an integer n not less than 3 and not greater than the chromatic number of S, we construct a graph admitting a triangular embedding in S and having chromatic number n