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The minimum degree of Ramsey-minimal graphs
Article first published online: 16 NOV 2006
DOI: 10.1002/jgt.20199
Copyright © 2006 Wiley Periodicals, Inc.
1097-0118/asset/cover.gif?v=1&s=747ee645df081de59c78864878c8bdb9daeca9a1 "Journal of Graph Theory")
Additional Information
How to Cite
Fox, J. and Lin, K. (2007), The minimum degree of Ramsey-minimal graphs. J. Graph Theory, 54: 167–177. doi: 10.1002/jgt.20199
Publication History
- Issue published online: 8 DEC 2006
- Article first published online: 16 NOV 2006
- Manuscript Revised: 29 MAY 2006
- Manuscript Received: 6 JUL 2005
- Abstract
- References
- Cited By
Keywords:
- Ramsey;
- critical;
- minimal;
- graph
Abstract
We write H → G if every 2-coloring of the edges of graph H contains a monochromatic copy of graph G. A graph H is G-minimal if H → G, but for every proper subgraph H′ of H, H′ ↛ G. We define s(G) to be the minimum s such that there exists a G-minimal graph with a vertex of degree s. We prove that s(Kk) = (k − 1)2 and s(Ka,b) = 2 min(a,b) − 1. We also pose several related open problems. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 167–177, 2007