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Biased graphs IV: Geometrical realizations
2003
Journal of combinatorial theory. Series B (Print)
A gain graph is a graph whose oriented edges are labelled invertibly from a group G; the gain group. A gain graph determines a biased graph and therefore has three natural matroids (as shown in Parts I and II): the bias matroid G has connected circuits; the complete lift matroid L 0 and its restriction to the edge set, the lift matroid L; have circuits not necessarily connected. We investigate representations of these matroids. Each has a canonical vector representation over any skew field F
doi:10.1016/s0095-8956(03)00035-2
fatcat:pdtpjm532jfy5ea3lzfqpzqoyi