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Connectivity in frame matroids. (English) Zbl 1170.05323
Summary: We discuss the relationship between the vertical connectivity of a biased graph 𝛺 and the Tutte connectivity of the frame matroid of 𝛺 (also known as the bias matroid of 𝛺).
MSC:
05C40Connectivity
05C22Signed and weighted graphs
05B35Matroids, geometric lattices (combinatorics)
References:
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[5]Tutte, W. T.: Connectivity in matroids, Canad. J. Math. 18, 1301-1324 (1966) · Zbl 0149.21501 · doi:10.4153/CJM-1966-129-2
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[8]Zaslavsky, T.: Vertices of localized imbalance in a biased graph, Proc. amer. Math. soc. 101, No. 1, 199-204 (1987) · Zbl 0622.05054 · doi:10.2307/2046575
[9]Zaslavsky, T.: Biased graphs. I. bias, balance, and gains, J. combin. Theory ser. B 47, No. 1, 32-52 (1989) · Zbl 0714.05057 · doi:10.1016/0095-8956(89)90063-4
[10]Zaslavsky, T.: Biased graphs whose matroids are special binary matroids, Graphs combin. 6, No. 1, 77-93 (1990) · Zbl 0786.05020 · doi:10.1007/BF01787483
[11]Zaslavsky, T.: Biased graphs. II. the three matroids, J. combin. Theory ser. B 51, No. 1, 46-72 (1991) · Zbl 0763.05096 · doi:10.1016/0095-8956(91)90005-5