Abstract
The Edmonds—Gallai decomposition theorem for matchings of finite or locally finite graphs is generalized to matchings of the kernel of an arbitrary graph.
Similar content being viewed by others
References
R. Aharoni, On an obstruction for perfect matchings,Combinatorica,4 (1984), 1–6.
R. Aharoni, A generalization of Tutte’s 1-factor theorem to countable graphs,J. Comb. Th. (B) 37 (1984), 199–209.
F. Bry andM. Las Vergnas, The Edmonds—Gallai decomposition for matchings in locally finite graphs,Combinatorica,2 (1982), 229–235.
J. Edmonds, Paths, trees and flowers,Can. J. Math.,17 (1965), 449–467.
T. Gallai, Maximale Systeme unabhängiger Kanten,Mat. Kut. Int. Közl.,9 (1964), 373–395.
T. Gallai, On factorization of graphs,Acta Math. Acad. Sci. Hungar.,1 (1950), 133–153.
F. Harary,Graph Theory, Addison—Wesley 1969.
L. Lovász, On the structure of factorizable graphs,Acta Math. Acad. Sci, Hung.,23 (1972), 179–185.
R. Schmidt,Ein Reduktionsverfahren für Weg-endliche Graphen, Dissertation, Hamburg 1982.
K. Steffens, Matchings in countable graphs,Can. J. Math.,29 (1976), 165–168.