Embedding Graphs into Larger Graphs: Results, Methods, and Problems

DOI10.1007/978-3-662-59204-5_14zbMath1443.05100arXiv1912.02068OpenAlexW2993699426MaRDI QIDQ3295275

Endre Szemerédi, Miklós Simmonovits

Publication date: 8 July 2020

Published in: Bolyai Society Mathematical Studies (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.02068

zbMATH Keywords

stabilityembeddingextremal graphsregularity lemmasemi-random methods

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Random graphs (graph-theoretic aspects) (05C80) Hypergraphs (05C65) Ramsey theory (05D10) Eulerian and Hamiltonian graphs (05C45) Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) (05D40) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

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Minimum degree conditions for tight Hamilton cycles, Dirac-type conditions for spanning bounded-degree hypertrees

Uses Software

• MathOverflow

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• Almost partitioning 2‐colored complete 3‐uniform hypergraphs into two monochromatic tight or loose cycles
• The hypergraph regularity method and its applications
• Regularity, uniformity, and quasirandomness
• Pósa's conjecture for graphs of order at least 2 × 10⁸
• The number of K _s,t -free graphs
• Note on Bipartite Graph Tilings
• A refinement of the Cameron-Erdős conjecture
• Powers of Hamilton Cycles in Pseudorandom Graphs
• On the General Position Subset Selection Problem
• On the Tree Packing Conjecture
• Nearly complete graphs decomposable into large induced matchings and their applications
• Stability results for random discrete structures
• The History of Degenerate (Bipartite) Extremal Graph Problems
• Extremal Results in Random Graphs
• Dynamic concentration of the triangle-free process
• Regular Partitions of Hypergraphs: Regularity Lemmas
• Sparse universal graphs for bounded‐degree graphs
• Fast monte-carlo algorithms for finding low-rank approximations
• On the Bollobás–Eldridge Conjecture for Bipartite Graphs
• Flag algebras
• Matchings in hypergraphs of large minimum degree
• Applications of the regularity lemma for uniform hypergraphs
• On an anti‐Ramsey problem of Burr, Erdős, Graham, and T. Sós
• Explicit constructions of triple systems for Ramsey–Turán problems
• Color critical hypergraphs with many edges
• Counting Independent Sets in Hypergraphs
• Digraphs
• The Representation of a Graph by Set Intersections
• A Holder Type Inequality for Symmetric Matrices with Nonnegative Entries
• The Hilbert-Schmidt Property for Embedding Maps between Sobolev Spaces
• On chromatic number of finite set-systems
• On Some Applications of Graph Theory to Geometry
• Maximal Sum-Free Sets of Group Elements
• SOME INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS
• On sets of integers containing no four elements in arithmetic progression
• On the number of complete subgraphs and circuits contained in graphs
• On Graphs that do not Contain a Thomsen Graph
• Maximal sum-free sets of elements of finite groups
• Sur les Ensembles de Sommets Indépendants Dans les Graphes Chromatiques Minimaux
• The Construction of Certain Graphs
• The Number of Finite Topologies
• Subgraphs with prescribed valencies
• On Some Applications of Graph Theory III
• Ramsey's Theorem for n-Parameter Sets
• On a Problem of Heilbronn†
• An extremal graph problem
• On a Problem of Heilbronn, II
• On a Problem of Heilbronn, III
• Polynomial extensions of van der Waerden’s and Szemerédi’s theorems
• ON THE NUMBER OF SUMS AND PRODUCTS
• Triple Systems Not Containing a Fano Configuration
• On Triple Systems with Independent Neighbourhoods
• Extensions of Turán's theorem on graphs
• On the maximal number of independent circuits in a graph
• Mantel's theorem for random hypergraphs
• Some remarks on the theory of graphs
• On a Problem of Heilbronn
• A Property of 4-Chromatic Graphs and some Remarks on Critical Graphs
• Some Theorems on Abstract Graphs
• On Certain Sets of Integers
• On a problem of K. Zarankiewicz
• On the theory of graphs
• On Sets of Integers Which Contain No Three Terms in Arithmetical Progression
• On Sets of Distances of n Points
• On a Problem of Sidon in Additive Number Theory and on Some Related Problems Addendum
• On the structure of linear graphs
• Optimal path and cycle decompositions of dense quasirandom graphs
• Packing, counting and covering Hamilton cycles in random directed graphs
• Quasi-random graphs
• Edge-decompositions of graphs with high minimum degree
• An anti-Ramsey theorem
• Strong Turán stability
• Ramsey-Turán theory
• Efficient testing of large graphs
• Proof of the Alon-Yuster conjecture
• The asymptotic number of triple systems not containing a fixed one
• Graph colouring and the probabilistic method
• Sum-free sets in Abelian groups.
• Crossing patterns of segments
• Vertex covers by edge disjoint cliques
• On 3-uniform hypergraphs without linear cycles
• Many \(T\) copies in \(H\)-free graphs
• Quasirandomness in hypergraphs
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