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Published in: Graph Theory and Combinatorial Biology (Balatonlelle, 1996), Bolyai Soc. Math. Stud. 7,
 

Summary: Published in: Graph Theory and Combinatorial Biology
(Balatonlelle, 1996), Bolyai Soc. Math. Stud. 7,
J´anos Bolyai Math. Soc., Budapest, 1999, 29­85.
The Colin de Verdi`ere graph parameter
(Preliminary version, March 1997)
Hein van der Holst1
, L´aszl´o Lov´asz2
, and Alexander Schrijver3
Contents
1 Introduction 3
1.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Some examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Basic facts 8
2.1 Transversality and the Strong Arnold Property . . . . . . . . . . . . . . . . 8
2.2 Monotonicity and components . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Clique sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Subdivision and Y transformation . . . . . . . . . . . . . . . . . . . . . . 16
2.5 The null space of M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3 Vector labellings 21

  

Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina

 

Collections: Mathematics