1

August 2017
Random Structures & Algorithms: Volume 51 Issue 1, August 2017

**Publisher:** John Wiley & Sons, Inc.

We determine to within a constant factor the threshold for the property that two random k-uniform hypergraphs with edge probability p have an edge-disjoint packing into the same vertex set. More generally, we allow the hypergraphs to have different densities. In the graph case, we prove a stronger result, on ...

**Keywords**:
random hypergraphs, packing

2

June 2017
Journal of Graph Theory: Volume 85 Issue 2, June 2017

**Publisher:** John Wiley & Sons, Inc.

We give a complete description of the set of triples α,β,γ of real numbers with the following property. There exists a constant K such that αn3+βn2+γn1-K is a lower bound for the matching number ï�źG of every connected subcubic graph G, where ni denotes the number of vertices of degree ...

**Keywords**:
matching, subcubic graph, polyhedron

3

May 2017
Random Structures & Algorithms: Volume 50 Issue 3, May 2017

**Publisher:** John Wiley & Sons, Inc.

We give two results for multicommodity flows in the d-dimensional hypercube Qd with independent random edge-capacities distributed like a random variable C where [C>0]>1/2. Firstly, with high probability as d∞, the network can support simultaneous multicommodity flows of volume close to E[C] between all antipodal vertex pairs. Secondly, with high ...

**Keywords**:
hypercube, multicommodity flow, capacity, random

4

November 2016
European Journal of Combinatorics: Volume 58 Issue C, November 2016

**Publisher:** Academic Press Ltd.

A class of graphs is called block-stable when a graph is in the class if and only if each of its blocks is. We show that, as for trees, for most n -vertex graphs in such a class, each vertex is in at most ( 1 + o ( 1 ...

5

October 2016
Distributed Computing: Volume 29 Issue 5, October 2016

**Publisher:** Springer-Verlag

We propose distributed algorithms for two well-established problems that operate efficiently under extremely harsh conditions. Our algorithms achieve state-of-the-art performance in a simple and novel way. Our algorithm for maximal independent set selection operates on a network of identical anonymous processors. The processor at each node has no prior information ...

6

October 2015
European Journal of Combinatorics: Volume 49 Issue C, October 2015

**Publisher:** Academic Press Ltd.

For a graph G , let f ( G ) be the largest integer k such that there are two vertex-disjoint subgraphs of G each on k vertices, both inducing the same number of edges. We prove that f ( G ) � n / 2 - o ( n ...

7

February 2015
European Journal of Combinatorics: Volume 44 Issue PA, February 2015

**Publisher:** Academic Press Ltd.

Given two random hypergraphs, or two random tournaments of order n , how much (or little) can we make them overlap by placing them on the same vertex set? We give asymptotic answers to this question.

8

January 2015
Journal of Combinatorial Theory Series B: Volume 110 Issue C, January 2015

**Publisher:** Academic Press, Inc.

Given two weighted k-uniform hypergraphs G, H of order n, how much (or little) can we make them overlap by placing them on the same vertex set? If we place them at random, how concentrated is the distribution of the intersection? The aim of this paper is to investigate these ...

**Keywords**:
Discrepancy, Hypergraphs

9

May 2014
Theory of Computing Systems: Volume 54 Issue 4, May 2014

**Publisher:** Springer-Verlag New York, Inc.

We consider problems related to the combinatorial game (Free-) Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations. We show that the minimum number of moves required to flood any given graph G is equal to the minimum, taken over ...

**Keywords**:
Computational complexity, Games on graphs, Graph colouring

10

July 2013
PODC '13: Proceedings of the 2013 ACM symposium on Principles of distributed computing

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 9

Downloads (6 Weeks): 1, Downloads (12 Months): 17, Downloads (Overall): 272

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Maximal Independent Set selection is a fundamental problem in distributed computing. A novel probabilistic algorithm for this problem has recently been proposed by Afek et al, inspired by the study of the way that developing cells in the fly become specialised. The algorithm they propose is simple and robust, but ...

**Keywords**:
beeping model, expected complexity, feedback, intercellular signalling, message complexity, mis, randomised algorithms

11

September 2012
Journal of Graph Theory: Volume 71 Issue 1, September 2012

**Publisher:** John Wiley & Sons, Inc.

For any graph H , let Forb*( H ) be the class of graphs with no induced subdivision of H . It was conjectured in [J Graph Theory, 24 (1997), 297–311] that, for every graph H , there is a function f H : ℕ→ℝ such that for every graph ...

**Keywords**:
bull, induced subgraphs, necklace, chi-bounded, coloring

12

September 2011
ESA'11: Proceedings of the 19th European conference on Algorithms

**Publisher:** Springer-Verlag

A colouring of a hypergraph's vertices is polychromatic if every hyperedge contains at least one vertex of each colour; the polychromatic number is the maximum number of colours in such a colouring. Its dual, the cover-decomposition number, is the maximum number of disjoint hyperedge-covers. In geometric settings, there is extensive ...

13

April 2011
Journal of Graph Theory: Volume 66 Issue 4, April 2011

**Publisher:** John Wiley & Sons, Inc.

Let G and H be two graphs of order n . If we place copies of G and H on a common vertex set, how much or little can they be made to overlap? The aim of this article is to provide some answers to this question, and to pose ...

**Keywords**:
discrepancy, graph intersections, subgraphs

14

August 2010
Discrete Mathematics: Volume 310 Issue 15-16, August, 2010

**Publisher:** Elsevier Science Publishers B. V.

Alon, et al. (2003) [1] proved that every graph with a large cut has a bipartition in which each vertex class contains correspondingly few edges. We prove an analogous result for partitions into k>=3 classes; along the way we prove a result for biased bipartitions.

**Keywords**:
Extremal graph theory, Max cut, Judicious partitions

15

November 2009
ACM Transactions on Algorithms (TALG): Volume 5 Issue 4, October 2009

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 4

Downloads (6 Weeks): 2, Downloads (12 Months): 12, Downloads (Overall): 274

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We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials, PCSP has scores that are arbitrary multivariate formal polynomials, or indeed take values in an arbitrary ring. ...

**Keywords**:
Exponential-time algorithm, discrete optimization, exact algorithm, generating function, partition function, constraint satisfaction

16

September 2009
Operations Research Letters: Volume 37 Issue 5, September, 2009

**Publisher:** Elsevier Science Publishers B. V.

Give random capacities C to the edges of the complete n-vertex graph. Consider the maximum flow @F"n that can be simultaneously routed between each source-destination pair. We prove that @F"n->@f in probability where the limit constant @f depends on the distribution of C in a simple way, and that asymptotically ...

**Keywords**:
Multicommodity flow, Graph colouring

17

December 2007
Discrete Optimization: Volume 4 Issue 3-4, December, 2007

**Publisher:** Elsevier Science Publishers B. V.

The class Max (r,2)-CSP, or simply Max 2-CSP, consists of constraint satisfaction problems with at most two r-valued variables per clause. For instances with n variables and m binary clauses, we present an O(nr^5^+^1^9^m^/^1^0^0)-time algorithm which is the fastest polynomial-space algorithm for many problems in the class, including Max Cut. ...

**Keywords**:
Exact algorithms, Max 2-CSP, Max 2-Sat, Linear-programming duality, Max Cut, Measure and conquer

18

May 2007
European Journal of Combinatorics: Volume 28 Issue 4, May, 2007

**Publisher:** Academic Press Ltd.

We sharpen a result of Hansel on separating set systems. We also extend a theorem of Spencer on completely separating systems by proving an analogue of Hansel's result.

19

May 2007
Journal of Graph Theory: Volume 55 Issue 1, May 2007

**Publisher:** John Wiley & Sons, Inc.

It is easily shown that every digraph with m edges has a directed cut of size at least m -4, and that 1-4 cannot be replaced by any larger constant. We investigate the size of the largest directed cut in acyclic digraphs, and prove a number of related results concerning ...

**Keywords**:
directed cut, extremal problems, directed and acyclic graphs, maximum cut

20

March 2007
Journal of Combinatorial Theory Series B: Volume 97 Issue 2, March, 2007

**Publisher:** Academic Press, Inc.

We prove results on the size of weakly and strongly separating set systems and matrices, and on cross-intersecting systems. As a consequence, we improve on a result of Katona and Szemeredi [G. Katona, E. Szemeredi, On a problem of graph theory, Studia Sci. Math. Hungar. 2 (1967) 23-28], who proved ...

**Keywords**:
Oriented graphs, Diameter, Separating systems, Weakly separating systems