论文信息 - The even cycle problem for directed graphs

The even cycle problem for directed graphs

If each arc in a strongly connected directed graph of minimum in- degree and outdegree at least 3 is assigned a weight 0 or 1, then the resulting weighted directed graph has a directed cycle of even total weight. This proves a conjecture made by L. Lovisz in 1975 and has applications to colour-critical hypergraphs, sign-nonsingular matrices, and permanents of matrices. MATHEMATICAL INSTITUTE, TECHNICAL UNIVERSITY OF DENMARK, DK-2800 LYNGBY,

Carsten Thomassen

[1] Charles H. C. Little,et al. An Extension of kasteleyn's method of enumerating the 1-factors of planar graphs , 1974 .

[2] Wayne Goddard,et al. Even Cycles in Directed Graphs , 1994, SIAM J. Discret. Math..

[3] C. Thomassen. Sign-Nonsingular Matrices and Even Cycles in Directed Graphs , 1986 .

[4] László Pyber,et al. Regular subgraphs of dense graphs , 1985, Comb..

[5] Shmuel Friedland,et al. Every 7-regular digraph contains an even cycle , 1989, J. Comb. Theory, Ser. B.

[6] P. Seymour. ON THE TWO-COLOURING OF HYPERGRAPHS , 1974 .

[7] Noga Alon,et al. Cycles of length 0 modulo k in directed graphs , 1989, J. Comb. Theory, Ser. B.

[8] László Lovász,et al. Matching structure and the matching lattice , 1987, J. Comb. Theory, Ser. B.

[9] Paul D. Seymour,et al. Characterization of even directed graphs , 1987, J. Comb. Theory, Ser. B.

[10] Mihalis Yannakakis,et al. Pfaffian orientations, 0-1 permanents, and even cycles in directed graphs , 1989, Discret. Appl. Math..

[11] Fuji Zhang,et al. Perfect matchings in hexagonal systems , 1985, Graphs Comb..

[12] Carsten Thomassen,et al. The Even Cycle Problem for Planar Digraphs , 1993, J. Algorithms.