an:06642335
Zbl 1347.05096
Traldi, Lorenzo
Notes on a theorem of Naji
EN
Discrete Math. 340, No. 1, 3217-3234 (2017).
00359891
2017
j
05C25 05C38 05B35 05C10 52B40
circle graph; graphic matroid; permutation graph; split decomposition
Summary: We present a new proof of an algebraic characterization of circle graphs due to \textit{W. Naji} [ibid. 54, 329--337 (1985; Zbl 0567.05033)].
For bipartite graphs, Naji's theorem is equivalent to an algebraic characterization of planar matroids due to \textit{J. Geelen} and \textit{B. Gerards} [J. Comb. Theory, Ser. B 103, No. 5, 642--646 (2013; Zbl 1408.05029)]. Naji's theorem also yields an algebraic characterization of permutation graphs.
Zbl 0567.05033; Zbl 1408.05029