Results 31 to 40 of about 14,274 (218)
Chromatic Turán problems and a new upper bound for the Turán density of $\mathcal{K}_4^-$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We consider a new type of extremal hypergraph problem: given an $r$-graph $\mathcal{F}$ and an integer $k≥2$ determine the maximum number of edges in an $\mathcal{F}$-free, $k$-colourable $r$-graph on $n$ vertices.
John Talbot
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Short proofs of some extremal results [PDF]
, 2013 We prove several results from different areas of extremal combinatorics, giving complete or partial solutions to a number of open problems. These results, coming from areas such as extremal graph theory, Ramsey theory and additive combinatorics, have ...
Beck +11 more
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On the quaternion projective space
Journal of Taibah University for Science, 2020 Apart from being a vital and exciting field in mathematics with interesting results, projective spaces have various applications in design theory, coding theory, physics, combinatorics, number theory and extremal combinatorial problems. In this paper, we
Y. Omar +4 more
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Hypergraphs with infinitely many extremal constructions
Discrete Analysis, 2023 Hypergraphs with infinitely many extremal constructions, Discrete Analysis 2023:18, 34 pp. A fundamental result in extremal graph theory, Turán's theorem, states that the maximal number of edges of a graph with $n$ vertices that does not contain a ...
Jianfeng Hou +4 more
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, 2014 Positional games are a branch of combinatorics, researching a variety of two-player games, ranging from popular recreational games such as Tic-Tac-Toe and Hex, to purely abstract games played on graphs and hypergraphs.
Krivelevich, Michael
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Polyhedral methods applied to extremal combinatorics problems
, 2014 Wir untersuchen Polytope, die zwei bekannte Probleme beschreiben: das Hypergraphen-Problem von Turán und die Vermutung von Frankl. Das Hypergraphen-Problem von Turán bestimmt die maximale Anzahl der r-Kanten in einem r-Hypergraph mit n Knoten, so dass der daraus entstandene r-Teil-Hypergraph keine Clique der Größe a enthält.
Annie Raymond
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Shattered Sets and the Hilbert Function [PDF]
, 2016 We study complexity measures on subsets of the boolean hypercube and exhibit connections between algebra (the Hilbert function) and combinatorics (VC theory). These connections yield results in both directions.
Moran, Shay, Rashtchian, Cyrus
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Pairwise Intersections and Forbidden Configurations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let $f_m(a,b,c,d)$ denote the maximum size of a family $\mathcal{F}$ of subsets of an $m$-element set for which there is no pair of subsets $A,B \in \mathcal{F}$ with $|A \cap B| \geq a$, $|\bar{A} \cap B| \geq b$, $|A \cap \bar{B}| \geq c$, and $|\bar{A}
Richard P. Anstee, Peter Keevash
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Extremes of the internal energy of the Potts model on cubic graphs [PDF]
, 2017 We prove tight upper and lower bounds on the internal energy per particle (expected number of monochromatic edges per vertex) in the anti-ferromagnetic Potts model on cubic graphs at every temperature and for all $q \ge 2$.
Davies, Ewan +3 more
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Generalized Ramsey–Turán density for cliques
Forum of Mathematics, SigmaWe study the generalized Ramsey–Turán function $\mathrm {RT}(n,K_s,K_t,o(n))$ , which is the maximum possible number of copies of $K_s$ in an n-vertex $K_t$ -free graph with independence number $o(n)$ . The case when $s=2$
Jun Gao +3 more
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