On minimal Folkman graphs
2001; Elsevier BV; Volume: 236; Issue: 1-3 Linguagem: Inglês
10.1016/s0012-365x(00)00445-3
ISSN1872-681X
AutoresTomasz Łuczak, Andrzej Ruciński, Sebastian Urbański,
Tópico(s)Advanced Graph Theory Research
ResumoFollowing the arrow notation, for a graph G and natural numbers a1,a2,…,ar we write G→(a1,a2,…,ar)v if for every coloring of the vertices of G with r colors there exists a copy of the complete graph Kai of color i for some i=1,2,…,r. We present some constructions of small graphs with this Ramsey property, but not containing large cliques. We also set bounds on the order of the smallest such graphs.
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