Observations on maps and δ-matroids
R. Bruce Richter
Discussiones Mathematicae Graph Theory, Tome 16 (1996), p. 197-205 / Harvested from The Polish Digital Mathematics Library
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Using a Δ-matroid associated with a map, Anderson et al (J. Combin. Theory (B) 66 (1996) 232-246) showed that one can decide in polynomial time if a medial graph (a 4-regular, 2-face colourable embedded graph) in the sphere, projective plane or torus has two Euler tours that each never cross themselves and never use the same transition at any vertex. With some simple observations, we extend this to the Klein bottle and the sphere with 3 crosscaps and show that the argument does not work in any other surface. We also show there are other Δ-matroids that one can associate with an embedded graph.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:270187 
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R. Bruce Richter. Observations on maps and δ-matroids. Discussiones Mathematicae Graph Theory, Tome 16 (1996) pp. 197-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1034/

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