10,194 research outputs found
Consistent random vertex-orderings of graphs
Given a hereditary graph property , consider distributions of
random orderings of vertices of graphs that are preserved
under isomorphisms and under taking induced subgraphs. We show that for many
properties the only such random orderings are uniform, and give
some examples of non-uniform orderings when they exist
Generalized Mom-structures and ideal triangulations of 3-manifolds with non-spherical boundary
The so-called Mom-structures on hyperbolic cusped 3-manifolds without
boundary were introduced by Gabai, Meyerhoff, and Milley, and used by them to
identify the smallest closed hyperbolic manifold. In this work we extend the
notion of a Mom-structure to include the case of 3-manifolds with non-empty
boundary that does not have spherical components. We then describe a certain
relation between such generalized Mom-structures, called protoMom-structures,
internal on a fixed 3-manifold N, and ideal triangulations of N; in addition,
in the case of non-closed hyperbolic manifolds without annular cusps, we
describe how an internal geometric protoMom-structure can be constructed
starting from Epstein-Penner or Kojima decomposition. Finally, we exhibit a set
of combinatorial moves that relate any two internal protoMom-structures on a
fixed N to each other.Comment: 38 pages, 19 figues; exposition style changed, particularly in
Section 2.2; minor content changes in Section 2.
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