159 research outputs found
Some Ramsey theorems for finite -colorable and -chromatic graphs
Given a fixed integer , we prove Ramsey-type theorems for the classes of
all finite ordered -colorable graphs, finite -colorable graphs, finite
ordered -chromatic graphs, and finite -chromatic graphs.Comment: 7 page
Symmetries and Ramsey properties of trees
AbstractIn this paper we show the extent to which a finite tree of fixed height is a Ramsey object in the class of trees of the same height can be measured by its symmetry group
Four Variations on Graded Posets
We explore the enumeration of some natural classes of graded posets,
including all graded posets, (2+2)- and (3+1)-avoiding graded posets,
(2+2)-avoiding graded posets, and (3+1)-avoiding graded posets. We obtain
enumerative and structural theorems for all of them. Along the way, we discuss
a situation when we can switch between enumeration of labeled and unlabeled
objects with ease, generalize a result of Postnikov and Stanley from the theory
of hyperplane arrangements, answer a question posed by Stanley, and see an old
result of Klarner in a new light.Comment: 28 page
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