Packing Odd Circuits in Eulerian Graphs

نویسندگان

James F. Geelen

Bertrand Guenin

چکیده

Let C be the clutter of odd circuits of a signed graph ðG;SÞ: For nonnegative integral edge-weights w; we are interested in the linear program minðwtx: xðCÞ51; for C 2 C; and x50Þ; which we denote by (P). The problem of solving the related integer program clearly contains the maximum cut problem, which is NP-hard. Guenin proved that (P) has an optimal solution that is integral so long as ðG;SÞ does not contain a minor isomorphic to odd-K5: We generalize this by showing that if ðG;SÞ does not contain a minor isomorphic to odd-K5 then (P) has an integral optimal solution and its dual has a half-integral optimal solution. # 2002 Elsevier Science (USA)

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