The crossing number of a projective graph is quadratic in the face--width

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Authors

HLINĚNÝ Petr SALAZAR Gelasio GITLER Isidoro LEANOS Jesus

Year of publication 2008
Type Article in Periodical
Magazine / Source Electronic Journal of Combinatorics
MU Faculty or unit

Faculty of Informatics

Citation
Web online paper
Field General mathematics
Keywords crossing number; projective plane; face-width
Description We show that for each integer g there is a constant Cg such that every graph that embeds in the projective plane with sufficiently large face-width r has crossing number at least Cgr^2 in the orientable surface Sg of genus g. As a corollary, we give a polynomial time constant factor approximation algorithm for the crossing number of projective graphs with bounded degree.
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