A lower bound for irredundant Ramsey numbers

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Given a graph G = (V, E), a vertex subset U ⊆ V is called irredundant if every vertex v ∈ U either has no neighbours in U or there exists a vertex w ∈ V\U such that v is the only neighbour of w in U. The irredundant Ramsey number s(m,n) is the smallest N such that any red-blue edge colouring of KN yields either an m-element irredundant subset in the blue graph or an n-element irredundant subset in the red graph. Using probabilistic methods we show that formula presented.

Original languageEnglish
Pages (from-to)185-192
Number of pages8
JournalDiscrete Mathematics
Issue number1-3
StatePublished - 15 Mar 1998


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