18 citations · 59 across the 14 of their papers we have counts for
15 papers
Measurable Regular Subgraphs
Matt Bowen, Clinton T. Conley, Felix Weilacher
We show that every -regular bipartite Borel graph admits a Baire measurable -regular spanning subgraph if and only if is odd or is even. This gives the first example…
Quasi-invariant measures concentrating on countable structures
Clinton Conley, Colin Jahel, Aristotelis Panagiotopoulos
Countable -structures whose isomorphism class supports a permutation invariant probability measure in the logic action have been characterized by Ackerma…
Local version of Vizing's theorem for multi-graphs
Clinton T. Conley, Jan Grebik, Oleg Pikhurko
Extending a result of Christiansen, we prove that every mutli-graph admits a proper edge colouring which is local, that is, $ϕ(e)\le \max\{d(x)+π(x…
One-ended spanning subforests and treeability of groups
Clinton T. Conley, Damien Gaboriau, Andrew S. Marks +1
We show that several new classes of groups are measure strongly treeable. In particular, finitely generated groups admitting planar Cayley graphs, elementarily free groups, and the…
Divisibility of Spheres with Measurable Pieces
Clinton T. Conley, Jan Grebík, Oleg Pikhurko
For an -tuple of special orthogonal matrices, we say that the Euclidean -dimensional sphere is -divisible if th…
Borel asymptotic dimension and hyperfinite equivalence relations
Clinton Conley, Steve Jackson, Andrew Marks +2
A long standing open problem in the theory of hyperfinite equivalence relations asks if the orbit equivalence relation generated by a Borel action of a countable amenable group is…
Measure reducibility of countable Borel equivalence relations
Clinton T. Conley, Benjamin D. Miller
We show that every basis for the countable Borel equivalence relations strictly above under measure reducibility is uncountable, thereby ruling out natural generaliz…
Measurable perfect matchings for acyclic locally countable Borel graphs
Clinton T. Conley, Benjamin D. Miller
We characterize the structural impediments to the existence of Borel perfect matchings for acyclic locally countable Borel graphs admitting a Borel selection of finitely many ends…
Incomparable actions of free groups
Clinton T. Conley, Benjamin D. Miller
Suppose that is a Polish space, is a countable Borel equivalence relation on , and is an -invariant Borel probability measure on . We consider the circumstance…
Equitable Colorings of Borel Graphs
Anton Bernshteyn, Clinton T. Conley
Hajnal and Szemerédi proved that if is a finite graph with maximum degree , then for every integer , has a proper coloring with colors in which ever…
Measurable realizations of abstract systems of congruences
Clinton T. Conley, Andrew S. Marks, Spencer T. Unger
An abstract system of congruences describes a way of partitioning a space into finitely many pieces satisfying certain congruence relations. Examples of abstract systems of congrue…
Distance from marker sequences in locally finite Borel graphs
Clinton T. Conley, Andrew S. Marks
We show that a locally finite Borel graph is nonsmooth if and only if it admits marker sequences which are "far" from every point. Our proof uses the Galvin-Prikry theorem and the…
Folner tilings for actions of amenable groups
Clinton T. Conley, Steve Jackson, David Kerr +3
We show that every probability-measure-preserving action of a countable amenable group G can be tiled, modulo a null set, using finitely many finite subsets of G ("shapes") with pr…
Hyperfiniteness and Borel combinatorics
Clinton Conley, Steve Jackson, Andrew Marks +2
We study the relationship between hyperfiniteness and problems in Borel graph combinatorics by adapting game-theoretic techniques introduced by Marks to the hyperfinite setting. We…
Brooks's theorem for measurable colorings
Clinton T. Conley, Andrew S. Marks, Robin Tucker-Drob
We generalize Brooks's theorem to show that if is a Borel graph on a standard Borel space of degree bounded by which contains no -cliques, then admits…