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Bulletin of the London Mathematical Society, ISSN 0024-6093, 12/2019, Volume 51, Issue 6, pp. 1015 - 1021
We use a variant of Bukh's random algebraic method to show that for every natural number k⩾2 there exists a natural number ℓ such that, for every n, there is a... 
05C35 (primary)
Journal Article
Discrete Mathematics, ISSN 0012-365X, 01/2020, Volume 343, Issue 1, p. 111641
A graph G is called H-induced-saturated if G does not contain an induced copy of H, but removing any edge from G creates an induced copy of H and adding any... 
05C35 | Saturation | Induced subgraph
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 06/2019, Volume 51, Issue 3, pp. 421 - 430
We show that if the second eigenvalue λ of a d‐regular graph G on n∈3Z vertices is at most εd2/(nlogn), for a small constant ε>0, then G contains a... 
05C35 (primary)
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 06/2019, Volume 99, Issue 3, pp. 757 - 777
Consider integers k,ℓ such that 0⩽ℓ⩽k2. Given a large graph G, what is the fraction of k‐vertex subsets of G which span exactly ℓ edges? When G is empty or... 
60C05 (secondary) | 05C35 | 05D40 (primary) | MATHEMATICS | MATRICES | SIZES | SMALL NUMBER | SINGULARITY | INDUCIBILITY | GRAPHS | Mathematics - Combinatorics
Journal Article
Mathematical Proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, 06/2019, pp. 1 - 34
Abstract We analyse the asymptotic extremal growth rate of the Betti numbers of clique complexes of graphs on n vertices not containing a fixed forbidden... 
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 12/2018, Volume 98, Issue 3, pp. 593 - 608
A bipartite graph H is said to have Sidorenko's property if the probability that the uniform random mapping from V(H) to the vertex set of any graph G is a... 
05C35 (primary) | MATHEMATICS | Mathematics - Combinatorics
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 02/2017, Volume 95, Issue 1, pp. 203 - 222
Given any integers s,t⩾2, we show that there exists some c=c(s,t)>0 such that any Ks,t‐free graph with average degree d contains a subdivision of a clique with... 
05C83 (secondary) | 05C35 (primary) | 05C38
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 04/2019, Volume 51, Issue 2, pp. 230 - 236
We show that the maximum number of triples on n points, if no three triples span at most five points, is (1±o(1))n2/5. More generally, let f(r)(n;k,s) be the... 
05B07 | 05C35 | 05D05 (primary) | MATHEMATICS | Mathematics - Combinatorics
Journal Article
Combinatorica, ISSN 0209-9683, 12/2018, Volume 38, Issue 6, pp. 1415 - 1436
Journal Article
Polycyclic Aromatic Compounds, ISSN 1040-6638, 2019, pp. 1 - 8
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 2019, Volume 39, Issue 4, pp. 937 - 950
We present some new constructive upper bounds based on product graphs for generalized vertex Folkman numbers. They lead to new upper bounds for some special... 
Ramsey number | 05C55 | Folkman number | 05C35
Journal Article
Discussiones Mathematicae Graph Theory, 11/2019, Volume 39, Issue 4, pp. 805 - 814
The Turán number of a graph H, denoted by ex(n, H), is the maximum number of edges in any graph on n vertices which does not contain H as a subgraph. Let Pk... 
Turán number | 2P7 | extremal graphs | 05C35
Journal Article
COMBINATORICA, ISSN 0209-9683, 11/2019, Volume 39, Issue 5, pp. 1081 - 1104
An embedding of a graph in 3-space is linkless if for every two disjoint cycles there exists an embedded ball that contains one of the cycles and is disjoint... 
05C10 | MATHEMATICS | 05C83 | 05C35 | Mathematics - Combinatorics
Journal Article
Combinatorica, ISSN 0209-9683, 4/2019, Volume 39, Issue 2, pp. 427 - 446
We study the diameter of LPS Ramanujan graphs X p,q . We show that the diameter of the bipartite Ramanujan graphs is greater than (4/3)log p (n)+O(1), where n... 
Mathematics, general | Mathematics | Combinatorics | 05C25 | 05C35 | MATHEMATICS
Journal Article
Combinatorica, ISSN 0209-9683, 2/2019, Volume 39, Issue 1, pp. 135 - 151
We provide sufficient conditions for the existence of long cycles in locally expanding graphs, and present applications of our conditions and techniques to... 
05D10 | Mathematics, general | Mathematics | 05C80 | Combinatorics | 05C35 | 05C57 | 05C38 | MATHEMATICS
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 02/2017, Volume 49, Issue 1, pp. 45 - 57
We call a graph G an (r,t)‐Ruzsa–Szemerédi graph if its edge set can be partitioned into t edge‐disjoint induced matchings, each of size r. These graphs were... 
05C35 | 05C70 (primary) | MATHEMATICS | TESTING SUBGRAPHS
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 12/2017, Volume 96, Issue 3, pp. 584 - 600
Frankl and Füredi conjectured in 1989 that the maximum Lagrangian of all r‐uniform hypergraphs of fixed size m is realised by the initial segment of the... 
05C65 | 05C31 | 90C35 (secondary) | 05D05 (primary) | 05C35 | MATHEMATICS | THEOREM | TURAN
Journal Article
Combinatorica, ISSN 0209-9683, 2/2019, Volume 39, Issue 1, pp. 215 - 237
A graph on n vertices is said to be C-Ramsey if every clique or independent set of the graph has size at most C logn. The only known constructions of Ramsey... 
Mathematics, general | Mathematics | 05D10 | Combinatorics | 05C35 | MATHEMATICS
Journal Article
Journal of Discrete Mathematical Sciences and Cryptography, ISSN 0972-0529, 11/2018, Volume 21, Issue 7-8, pp. 1523 - 1528
For two graphs F 1 and F 2 , the Ramsey number R(F 1 , F 2 ) is the smallest positive integer r such that for every graph G on r vertices, G contains F 1 as a... 
Wheel | 05C55 | Ramsey number | 05C35 | Chord | Cycle
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 02/2018, Volume 97, Issue 1, pp. 77 - 97
Erdős [Israel J. Math. 2 (1964) 183–190] characterised those hypergraphs F that have to appear in any sufficiently large hypergraph H of positive density. We... 
05C65 | 05C35 (primary) | 05C80 (secondary) | MATHEMATICS | REGULAR PARTITIONS
Journal Article
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