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- Title
On Pattern Ramsey Numbers of Graphs.
- Authors
Jamison, Robert E.; West, Douglas B.
- Abstract
Acolor patternis a graph whose edges are partitioned into color classes. A familyFof color patterns is aRamsey familyif there is some integerNsuch that every edge-coloring ofK N has a copy of some pattern inF. The smallest suchNis the(pattern) Ramsey numberR(F) ofF. The classical Canonical Ramsey Theorem of Erdös and Rado [4] yields an easy characterization of the Ramsey families of color patterns. In this paper we determineR(F) for all families consisting of equipartitioned stars, and we prove thatwhenFconsists of a monochromatic star of sizesand a polychromatic triangle.
- Subjects
GRAPHIC methods; GRAPH theory; RINGS of integers; ALGEBRAIC number theory; RING theory
- Publication
Graphs & Combinatorics, 2004, Vol 20, Issue 3, p333
- ISSN
0911-0119
- Publication type
Article
- DOI
10.1007/s00373-004-0562-y