| Title:
|
On a generalization of perfect $b$-matching (English) |
| Author:
|
Šándorová, Ľubica |
| Author:
|
Trenkler, Marián |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
116 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
380-384 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
perfect $b$-matching |
| Keyword:
|
beta-non-negative and beta-positive graphs |
| Keyword:
|
systems of linear equations |
| MSC:
|
05C50 |
| MSC:
|
68E10 |
| MSC:
|
68R10 |
| idZBL:
|
Zbl 0735.68068 |
| idMR:
|
MR1146395 |
| DOI:
|
10.21136/MB.1991.126032 |
| . |
| Date available:
|
2009-09-24T20:47:22Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126032 |
| . |
| Reference:
|
[1] C. Berge: Regularisable Graphs II.Discrete Math. 23 (1978), 91 - 95. Zbl 0392.05051, MR 0523404, 10.1016/0012-365X(78)90108-5 |
| Reference:
|
[2] S. Jezný M. Trenkler: Characterization of Magic Graphs.Czech. Math. J. 33 (1983), 435-438. MR 0718926 |
| Reference:
|
[3] R. H. Jeurissen: The Incidence Matrix and Labellings of a Graph.J. Comb. Theory B 30 (1981), 290-301. Zbl 0409.05042, MR 0624546, 10.1016/0095-8956(81)90047-2 |
| Reference:
|
[4] B. Grünbaum: Convex Polytopes.Interscience, London 1967. MR 0226496 |
| Reference:
|
[5] L. Lovász M. D. Plummer: Matching Theory.Akadémiai kiadó, Budapest 1986. MR 0859549 |
| Reference:
|
[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 |
| Reference:
|
[7] B. M. Stewart: Magic Graphs.Canad. J. Math. 18 (1966), 1031-1059. Zbl 0149.21401, MR 0197358, 10.4153/CJM-1966-104-7 |
| . |
