On the 1-chromatic number of nonorientable surfaces with large genus

Authors:
Vladimir P. Korzhik
Affiliations:
National University of Chernivtsi, Chernivtsi, Ukraine and Institute of Applied Problems of Mechanics and Mathematics, National Academy of Science of Ukraine, Lviv, Ukraine
Venue:
Journal of Combinatorial Theory Series B
Year:
2012

Citing 5
Cited 0

Topological graph theory

Topological graph theory
A lower bound for the one-chromatic number of a surface

Journal of Combinatorial Theory Series B
A tighter bounding interval for the 1-chromatic number of a surface

Discrete Mathematics
A possibly infinite series of surfaces with known 1-chromatic number

Discrete Mathematics
An infinite series of surfaces with known 1-chromatic number

Journal of Combinatorial Theory Series B

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Abstract

The 1-chromatic number @g"1(S) of a surface S is the maximum chromatic number of all graphs which can be drawn on S so that each edge is crossed by no more than one other edge. It is proved that:(a)There is an integer Q0 such thatM(N"q)-1==Q, where N"q is the nonorientable surface of genus q and M(N"q) is Ringel@?s upper bound on @g"1(N"q); (b)@g"1(N"q)=M(N"q) for about 7/12 of all nonorientable surfaces N"q. The results are obtained by using index one current graphs.