Geodesic
Observations on maps and δ-matroids
Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 2, pp. 197-205

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: Δ-matroids, graph embeddings, A-trails 
@article{DMGT_1996_16_2_a9,
     author = {Richter, R.},
     title = {Observations on maps and \ensuremath{\delta}-matroids},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {197--205},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_1996_16_2_a9/}
}
TY  - JOUR
AU  - Richter, R.
TI  - Observations on maps and δ-matroids
JO  - Discussiones Mathematicae. Graph Theory
PY  - 1996
SP  - 197
EP  - 205
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_1996_16_2_a9/
LA  - en
ID  - DMGT_1996_16_2_a9
ER  - 
%0 Journal Article
%A Richter, R.
%T Observations on maps and δ-matroids
%J Discussiones Mathematicae. Graph Theory
%D 1996
%P 197-205
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_1996_16_2_a9/
%G en
%F DMGT_1996_16_2_a9
Richter, R. Observations on maps and δ-matroids. Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 2, pp. 197-205. http://geodesic.mathdoc.fr/item/DMGT_1996_16_2_a9/