Abstract
Let G be a bipartite graph with a bicoloration {A, B}, \A\ = \B\, and let w : E(G) → K where K is a finite abelian group with k elements. For a subset S ⊆ E(G) let w(S) = Πe∈S w(e). A perfect matching M ⊆ E(G) is a w-matching if w(M) = 1. It is shown that if deg(a) ≥ d for all a ∈ A, then either G has no w-matchings, or G has at least (d - k + 1)! w-matchings.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 285-290 |
| Number of pages | 6 |
| Journal | Journal of Algebraic Combinatorics |
| Volume | 7 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1998 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics
Keywords
- Bipartite matching
- Digraph
- Finite abelian group
- Group algebra
- Olson's Theorem