Observations on maps and δ-matroids

• Autorzy: R. Bruce Richter
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Δ-matroids; graph embeddings; A-trails

Kategorie tematyczne

• 05B35: Matroids, geometric lattices
• 05C10: Planar graphs; geometric and topological aspects of graph theory

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1996
• Tom: 16
• Numer: 2
• Strony: 197-205

Daty

wydano

1996

otrzymano

1996-07-22

poprawiono

1996-10-20

Twórcy

autor

R. Bruce Richter

• Department of Mathematics and Statistics, Carleton University, Ottawa Canada K1H 8H1

Bibliografia

• [1] L.D. Andersen, A. Bouchet and W. Jackson, Orthogonal A-trails of 4-regular graphs embedded in surfaces of low genus, J. Combin. Theory (B) 66 (1996) 232-246, doi: 10.1006/jctb.1996.0017.
• [2] A. Bouchet, Maps and Δ-matroids, Discrete Math. 78 (1989) 59-71, doi: 10.1016/0012-365X(89)90161-1.
• [3] A. Bouchet, Greedy algorithm and symmetric matroids, Math. Prog. 38 (1987) 147-159, doi: 10.1007/BF02604639.
• [4] A. Kotzig, Eulerian lines in finite 4-valent graphs and their transformations, in: Theory of Graphs (P. Erdős and G. Katona, eds.) North-Holland, Amsterdam (1968) 219-230.
• [5] R.B. Richter, Spanning trees, Euler tours, medial graphs, left-right paths and cycle spaces, Discrete Math. 89 (1991) 261-268, doi: 10.1016/0012-365X(91)90119-M.
• [6] E. Tardos, Generalized matroids and supermodular colorings, in Matroid Theory (Szeged 1982), North- Holland, Amsterdam (1985) 359-382.
• [7] T. Zaslavsky, Biased graphs I, J. Combin. Theory (B) 47 (1989) 32-52, doi: 10.1016/0095-8956(89)90063-4.

Identyfikatory

DOI

10.7151/dmgt.1034