论文信息 - Biased graphs. I. Bias, balance, and gains

Biased graphs. I. Bias, balance, and gains

A biased graph is a graph together with a class of cirles (simple closed paths), called balanced, such that no theta subgraph contains exactly two balanced circles. A gain graph is a graph in which each edge has a gain (a label from a group so that reversing the direction inverts the gain); a circle is balanced if its edge gain product is 1; this defines a biased graph. We initiate a series devoted to biased graphs and their matroids. Here we study properties of balance and also subgraphs and contractions of biased and gain graphs.

Thomas Zaslavsky | T. Zaslavsky

[1] Thomas Zaslavsky,et al. The biased graphs whose matroids are binary , 1987, J. Comb. Theory B.

[2] Thomas Zaslavsky,et al. Chromatic invariants of signed graphs , 1982, Discret. Math..

[3] Laurence R. Matthews. Matroids from directed graphs , 1978, Discret. Math..

[4] Thomas Zaslavsky,et al. Signed graph coloring , 1982, Discret. Math..

[5] J. M. S. Simões-Pereira. On matroids on edge sets of graphs with connected subgraphs as circuits II , 1975, Discret. Math..

[6] Michael Doob,et al. An interrelation between line graphs, eigenvalues, and matroids , 1973 .

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

[8] Thomas A. Dowling,et al. A class of geometric lattices based on finite groups , 1973 .

[9] Thomas Zaslavsky,et al. Characterizations of signed graphs , 1981, J. Graph Theory.

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

[11] W. T. Tutte. Lectures on matroids , 1965 .

[12] Thomas Zaslavsky,et al. The Geometry of Root Systems and Signed Graphs , 1981 .

[13] J. M. S. Simões Pereira,et al. On subgraphs as matroid cells , 1972 .