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Displaying similar documents to “Measure-theoretic unfriendly colorings”

Constant Sum Partition of Sets of Integers and Distance Magic Graphs

Sylwia Cichacz, Agnieszka Gőrlich (2018)

Discussiones Mathematicae Graph Theory

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Let A = {1, 2, . . . , tm+tn}. We shall say that A has the (m, n, t)-balanced constant-sum-partition property ((m, n, t)-BCSP-property) if there exists a partition of A into 2t pairwise disjoint subsets A1, A2, . . . , At, B1, B2, . . . , Bt such that |Ai| = m and |Bi| = n, and ∑a∈Ai a = ∑b∈Bj b for 1 ≤ i ≤ t and 1 ≤ j ≤ t. In this paper we give sufficient and necessary conditions for a set A to have the (m, n, t)-BCSP-property in the case when m and n are both even. We use this result...

Note on partitions of planar graphs

Izak Broere, Bonita S. Wilson, Jozef Bucko (2005)

Discussiones Mathematicae Graph Theory

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Chartrand and Kronk in 1969 showed that there are planar graphs whose vertices cannot be partitioned into two parts inducing acyclic subgraphs. In this note we show that the same is true even in the case when one of the partition classes is required to be triangle-free only.

A note on uniquely H-colourable graphs

Anthony Bonato (2007)

Discussiones Mathematicae Graph Theory

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For a graph H, we compare two notions of uniquely H-colourable graphs, where one is defined via automorphisms, the second by vertex partitions. We prove that the two notions of uniquely H-colourable are not identical for all H, and we give a condition for when they are identical. The condition is related to the first homomorphism theorem from algebra.

Some additions to the theory of star partitions of graphs

Francis K. Bell, Dragos Cvetković, Peter Rowlinson, Slobodan K. Simić (1999)

Discussiones Mathematicae Graph Theory

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This paper contains a number of results in the theory of star partitions of graphs. We illustrate a variety of situations which can arise when the Reconstruction Theorem for graphs is used, considering in particular galaxy graphs - these are graphs in which every star set is independent. We discuss a recursive ordering of graphs based on the Reconstruction Theorem, and point out the significance of galaxy graphs in this connection.

An Alpern tower independent of a given partition

James T. Campbell, Jared T. Collins, Steven Kalikow, Raena King, Randall McCutcheon (2015)

Colloquium Mathematicae

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Given a measure-preserving transformation T of a probability space (X,ℬ,μ) and a finite measurable partition ℙ of X, we show how to construct an Alpern tower of any height whose base is independent of the partition ℙ. That is, given N ∈ ℕ, there exists a Rokhlin tower of height N, with base B and error set E, such that B is independent of ℙ, and TE ⊂ B.

On restricted measurability

A. K. Mookhopadhyaya (1966)

Annales de l'institut Fourier

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Dans cet article, on étudie, certains résultats sur la mesurabilité restreinte [Trevor J. Mc Minn, Restricted Measurability, (1948), vol. 54, July-Dec., 1105] et à l’aide de cette notion, on construit une mesure de Radon analogue à celle de Mr. Sion [A Characterization of weak convergence, (1964), vol. 14, no 3, 1059] et on établit certaines de ses propriétés.