Abstract
Balanceable clutters are clutters whose bipartite representation contains no odd wheel and no odd 3-path configuration as induced subgraph (this is Truemper’s characterization of balanceable matrices). In this paper we study a proper subclass of balanceable clutters called quasi-graphical defined by forbidding one-sided even wheels and one-sided even 3-path configurations. We characterize Mengerian quasi-graphical clutters and, as a consequence, we show that a recent conjecture in [5] is true for quasi-graphical clutters.
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References
Apollonio, N.: Integrality properties of edge path tree families. Discrete Mathematics 309, 4181–4184 (2009)
Apollonio, N., Caramia, M.: A superclass of Edge-Path-Tree graphs with few cliques. Operations Research Letters (in press, 2009), doi:10.1016/j.orl.2009.05.002
Apollonio, N., Caramia, M.: A local structure result for line graphs of strong quasi-graphical matrices. Technical Report DII RR-08.09, University of Rome Tor Vergata, http://dspace.uniroma2.it/dspace/handle/2108/655
Conforti, M., Gerards, A.M.H., Kapoor, A.: A Theorem of Truemper. Combinatorica 20, 15–26 (2000)
Cornuéjols, G., Guenin, B., Margot, F.: The Packing Property. Mathematical Programming 89, 113–126 (2000)
Cornuéjols, G.: Combinatorial Optimization. Packing and Covering. SIAM, CBMS–NSF, Philadelphia (2001)
Fournier, J.-C.: Hypergraphes de Chaines d’ Aretes d’un Arbre. Discrete Mathematics 43, 29–36 (1983)
Golumbic, M.C., Jamison, R.E.: The Edge Intersection Graphs of Paths in a Tree. Journal of Combinatorial Theory, Series B 38, 8–22 (1985)
Schrijver, A.: Theory of Linear and Integer Programming. Wiley, Chichester (1986)
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© 2009 Springer-Verlag Berlin Heidelberg
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Apollonio, N., Caramia, M. (2009). Integrality Properties of Certain Special Balanceable Families. In: Fiala, J., Kratochvíl, J., Miller, M. (eds) Combinatorial Algorithms. IWOCA 2009. Lecture Notes in Computer Science, vol 5874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10217-2_8
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DOI: https://doi.org/10.1007/978-3-642-10217-2_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10216-5
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