1,495 research outputs found
Spectra of Monadic Second-Order Formulas with One Unary Function
We establish the eventual periodicity of the spectrum of any monadic
second-order formula where:
(i) all relation symbols, except equality, are unary, and
(ii) there is only one function symbol and that symbol is unary
Large stars with few colors
A recent question in generalized Ramsey theory is that for fixed positive
integers , at least how many vertices can be covered by the vertices
of no more than monochromatic members of the family in every edge
coloring of with colors. This is related to an old problem of Chung
and Liu: for graph and integers what is the smallest positive
integer such that every coloring of the edges of with
colors contains a copy of with at most colors. We answer this question
when is a star and is either or generalizing the well-known
result of Burr and Roberts
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