The crossing number of the generalized Petersen graph P[3k,k]

Title:

The crossing number of the generalized Petersen graph P[3k,k]

Creator:

Stanley and Gauci, John Baptist

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:c13c404d-1c11-426b-a6b9-17bb2764e782
uuid:c13c404d-1c11-426b-a6b9-17bb2764e782
doi:10.21136/MB.2003.134001

Subject:

graph, drawing, crossing number, generalized Petersen graph, and Cartesian product

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

ct. Guy and Harary (1967) have shown that, for k > 3, the graph P[2k, k] is homeomorphic to the Möbius ladder M2k, so that its crossing number is one; it is well known that P[2k, 2] is planar. Exoo, Harary and Kabell (1981) have shown hat the crossing number of P[2k + 1, 2] is three, for k ≥ 2. Fiorini (1986) and Richter and Salazar (2002) have shown that P[9, 3] has crossing number two and that P[3k, 3] has crossing number k, provided k ≥ 4. We extend this result by showing that P[3k, k] also has crossing number k for all k ≥ 4.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

337-347

Source:

Mathematica bohemica | 2003 Volume:128 | Number:4

Harvested from:

CDK

Metadata only:

false