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MINORS IN WEIGHTED GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  01 June 2008

CEZAR JOIŢA  and
DANIELA JOIŢA
CEZAR JOIŢA*
Affiliation:
Institute of Mathematics of the Romanian Academy, PO Box 1-764, Bucharest 014700, Romania (email: [email protected])
DANIELA JOIŢA
Affiliation:
Titu Maiorescu University, Calea Vacaresti nr. 187, sector 4, Bucharest 040056, Romania (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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We define the notion of minor for weighted graphs. We prove that with this minor relation, the set of weighted graphs is directed. We also prove that, given any two weights on a connected graph with the same total weight, we can transform one into the other using a sequence of edge subdivisions and edge contractions.

Keywords

graph minorsweighted graphs

MSC classification

Secondary: 05C83: Graph minors
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 3 , June 2008 , pp. 455 - 464
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Lovász, L., ‘Graph minor theory’, Bull. Amer. Math. Soc. (N.S.) 43(1) (2006), 75–86.Google Scholar
[2]Robertson, N. and Seymour, P. D., ‘Graph minors. XX. Wagner’s conjecture’, J. Combin. Theory Ser. B 92(2) (2004), 325–357.CrossRefGoogle Scholar