论文信息 - Detecting minors in matroids through triangles - 字舞流文

Detecting minors in matroids through triangles

Abstract In this note we investigate some matroid minor structure results. In particular, we present sufficient conditions, in terms of triangles, for a matroid to have either U 2 , 4 or F 7 or M ( K 5 ) as a minor.

Jorge L. Ramírez Alfonsín | Daniel Gonçalves | Boris Albar | D. Gonçalves | J. R. Alfonsín | Boris Albar

[1] Swastik Kopparty,et al. TO PLANAR GRAPHS , 2010 .

[2] G. Dirac. A Property of 4-Chromatic Graphs and some Remarks on Critical Graphs , 1952 .

[3] Eran Nevo,et al. On embeddability and stresses of graphs , 2004, Comb..

[4] Paul D. Seymour,et al. Decomposition of regular matroids , 1980, J. Comb. Theory, Ser. B.

[5] Paul D. Seymour,et al. Matroids and Multicommodity Flows , 1981, Eur. J. Comb..

[6] Daniel Gonçalves,et al. On triangles in Kr ‐minor free graphs , 2018, J. Graph Theory.

[7] James G. Oxley,et al. Matroid theory , 1992 .

[8] W. Mader. Homomorphiesätze für Graphen , 1968 .

[9] J.-C. Fournier. A characterization of binary geometries by a double elimination axiom , 1981, J. Comb. Theory, Ser. B.

[10] James G. Oxley,et al. A characterization of the ternary matroids with no M(K4)-minor , 1987, J. Comb. Theory, Ser. B.

[11] Boris Albar,et al. On triangles in K_r-minor free graphs , 2013, 1304.5468.

[12] Tom Brylawski,et al. A combinatorial model for series-parallel networks , 1971 .