Perfect matchings and K1,p-restricted graphs
-
Pavel A. Irzhavski
and
Yury L. Orlovich
Abstract
A graph is called K1,p-restricted (p ≥ 3) if for every vertex of the graph there are at least p − 2 edges between any p of its neighbours. We establish sufficient conditions for the existence of a perfect matching in K1,p-restricted graphs in terms of their connectivity and vertex degrees. These conditions imply, in particular, the classical Petersen’s result: any 2-edge-connected 3-regular graph contains a perfect matching.
Acknowledgment
The authors are obliged to the referee for useful comments and concrete advice, which contributed to the improvement of the text of this paper.
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Articles in the same Issue
- Frontmatter
- Group polynomials over rings
- Maximum subclasses in classes of linear automata over finite fields
- Using binary operations to construct a transitive set of block transformations
- Perfect matchings and K1,p-restricted graphs
- On the waiting times to repeated hits of cells by particles for the polynomial allocation scheme
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Articles in the same Issue
- Frontmatter
- Group polynomials over rings
- Maximum subclasses in classes of linear automata over finite fields
- Using binary operations to construct a transitive set of block transformations
- Perfect matchings and K1,p-restricted graphs
- On the waiting times to repeated hits of cells by particles for the polynomial allocation scheme
- Semibinomial conditionally nonlinear autoregressive models of discrete random sequences: probabilistic properties and statistical parameter estimation
