Mengerian quasi-graphical families and clutters

Authors:
Nicola Apollonio;Massimiliano Caramia
Affiliations:
Istituto per le Applicazioni del Calcolo, M. Picone, C.N.R., Via dei Taurini, 19 00185 Roma, Italy;Dipartimento di Ingegneria dell'Impresa, University of Rome "Tor Vergata", Via del Politecnico 1, 00133 Roma, Italy
Venue:
European Journal of Combinatorics
Year:
2013

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Abstract

Balanceable clutters are clutters whose bipartite representation contains no odd wheel and no odd 3-path configuration as an 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 Cornuejols et al. (2000) [7] is true for quasi-graphical clutters.