Graphs with no induced wheel and no induced antiwheel

A wheel is a graph that consists of a chordless cycle of length at least 4 plus a vertex with at least three neighbors on the cycle. An antiwheel is the complementary graph of a wheel. It was shown recently that detecting induced wheels is an NP-complete problem. In contrast, it is shown here that graphs that contain no wheel and no antiwheel have a very simple structure and consequently can be recognized in polynomial time.

[1]  Kristina Vuskovic,et al.  The world of hereditary graph classes viewed through Truemper configurations , 2013, Surveys in Combinatorics.

[2]  Paul D. Seymour,et al.  Recognizing Berge Graphs , 2005, Comb..

[3]  Nicolas Trotignon,et al.  Algorithms for Perfectly Contractile Graphs , 2005, SIAM J. Discret. Math..

[4]  N. Mahadev,et al.  Threshold graphs and related topics , 1995 .

[5]  Russell Merris,et al.  Split graphs , 2003, Eur. J. Comb..

[6]  Peter L. Hammer,et al.  The splittance of a graph , 1981, Comb..

[7]  Peter L. Hammer,et al.  Difference graphs , 1990, Discret. Appl. Math..

[8]  Klaus Truemper,et al.  Alpha-balanced graphs and matrices and GF(3)-representability of matroids , 1982, J. Comb. Theory, Ser. B.

[9]  Paul D. Seymour,et al.  The three-in-a-tree problem , 2010, Comb..

[10]  Nicolas Trotignon,et al.  Detecting wheels , 2013, ArXiv.