论文信息 - Signed analogs of bipartite graphs

Signed analogs of bipartite graphs

Abstract We characterize the edge-signed graphs in which every ‘significant’ positive closed walk (or combination of walks) has even length, under seven different criteria for significance, and also those edge-signed graphs whose double covering graph is bipartite. If the property of even length is generalized to positivity in a second edge signing, the characterizations generalize as well. We also characterize the edge-signed graphs with the smallest nontrivial chromatic numbers.

Thomas Zaslavsky

[1] Sóstenes Lins. Combinatorics of orientation reversing polygons , 1985 .

[2] Thomas Zaslavsky,et al. Orientation embedding of signed graphs , 1992, J. Graph Theory.

[3] Sóstenes Lins. Graph-encoded maps , 1982, J. Comb. Theory, Ser. B.

[4] Thomas Zaslavsky,et al. Biased graphs. I. Bias, balance, and gains , 1989, J. Comb. Theory, Ser. B.

[5] Klaus Truemper,et al. Alpha-balanced graphs and matrices and GF(3)-representability of matroids , 1982, J. Comb. Theory, Ser. B.

[6] Thomas Zaslavsky,et al. Biased graphs. II. The three matroids , 1991, J. Comb. Theory, Ser. B.

[7] F. Harary. On local balance and $N$-balance in signed graphs. , 1955 .

[8] F. Harary. On the notion of balance of a signed graph. , 1953 .

[9] Gerhard Ringel,et al. The combinatorial map color theorem , 1977, J. Graph Theory.

[10] Saul Stahl,et al. Generalized Embedding Schemes , 1978, J. Graph Theory.

[11] W. Leveque,et al. On asymmetric approximations. , 1953 .