Article

Full entry | PDF   (0.6 MB)
Keywords:
perfect $b$-matching; beta-non-negative and beta-positive graphs; systems of linear equations
Summary:
The paper is concerned with the existence of non-negative or positive solutions to $Af=\beta$, where $A$ is the vertex-edge incidence matrix of an undirected graph. The paper gives necessary and sufficient conditions for the existence of such a solution.
References:
[1] C. Berge: Regularisable Graphs II. Discrete Math. 23 (1978), 91 - 95. DOI 10.1016/0012-365X(78)90108-5 | MR 0523404 | Zbl 0392.05051
[2] S. Jezný M. Trenkler: Characterization of Magic Graphs. Czech. Math. J. 33 (1983), 435-438. MR 0718926
[3] R. H. Jeurissen: The Incidence Matrix and Labellings of a Graph. J. Comb. Theory B 30 (1981), 290-301. DOI 10.1016/0095-8956(81)90047-2 | MR 0624546 | Zbl 0409.05042
[4] B. Grünbaum: Convex Polytopes. Interscience, London 1967. MR 0226496
[5] L. Lovász M. D. Plummer: Matching Theory. Akadémiai kiadó, Budapest 1986. MR 0859549
[6] Ľ. Šándorová M. Trenkler: On a Generalization of Magic Graphs. Proc. of the 7th Hungarian Colloquium on Combinatorics, North Holland, 1988, 447-452. MR 1221584
[7] B. M. Stewart: Magic Graphs. Canad. J. Math. 18 (1966), 1031-1059. DOI 10.4153/CJM-1966-104-7 | MR 0197358 | Zbl 0149.21401

Partner of