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Distinguishing number of countable homogeneous relational structures
, 2010
"... The distinguishing number of a graph G is the smallest positive integer r such that G has a labeling of its vertices with r labels for which there is no nontrivial automorphism of G preserving these labels. In early work, Michael Albertson and Karen Collins computed the distinguishing number for va ..."
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The distinguishing number of a graph G is the smallest positive integer r such that G has a labeling of its vertices with r labels for which there is no nontrivial automorphism of G preserving these labels. In early work, Michael Albertson and Karen Collins computed the distinguishing number for various finite graphs, and more recently Wilfried Imrich, Sandi Klavzar and Vladimir Trofimov computed the distinguishing number of some infinite graphs, showing in particular that the Random Graph has distinguishing number 2. We compute the distinguishing number of various other finite and countable homogeneous structures, including undirected and directed graphs, and posets. We show that this number is in most cases two or infinite, and besides a few exceptions conjecture that this is so for all primitive homogeneous countable structures.
Some maximal subgroups of infinite symmetric groups
 J. London Math. Soc
, 1990
"... THIS paper concerns maximal subgroups of symmetric groups on infinite, usually countable, sets. Our main aim is to give examples of maximal subgroups which could claim to be almost stabilisers of familiar combinatorial ..."
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THIS paper concerns maximal subgroups of symmetric groups on infinite, usually countable, sets. Our main aim is to give examples of maximal subgroups which could claim to be almost stabilisers of familiar combinatorial