Corpus ID: 237940162

Regular decomposition of the edge set of graphs with applications

@inproceedings{Csaba2021RegularDO,
  title={Regular decomposition of the edge set of graphs with applications},
  author={B{\'e}la Csaba},
  year={2021}
}
We introduce a new method for decomposing the edge set of a graph, and use it to replace the Regularity lemma of Szemerédi in some graph embedding problems. An algorithmic version is also given. 

References

SHOWING 1-10 OF 28 REFERENCES
Szemeredi''s Regularity Lemma and its applications in graph theory
Szemer\''edi''s Regularity Lemma is an important tool in discrete mathematics. It says that, in some sense, all graphs can be approximated by random-looking graphs. Therefore the lemma helps inExpand
The Algorithmic Aspects of the Regularity Lemma
TLDR
The computational difficulty of finding a regular partition is demonstrated; it is shown that deciding if a given partition of an input graph satisfies the properties guaranteed by the lemma is co-NP-complete; and it is proved that despite this difficulty the regularity lemma can be made constructive. Expand
Triple systems with no six points carrying three triangles
  • Combinatorics (Keszthely, 1976), 18
  • 1978
The regularity method for graphs with few 4‐cycles
We develop a sparse graph regularity method that applies to graphs with few 4-cycles, including new counting and removal lemmas for 5-cycles in such graphs. Some applications include: * EveryExpand
Bounds for graph regularity and removal lemmas
TLDR
It is shown that a weak partition with approximation parameter Epsilon may require as many as 2^{\Omega}(\epsilon^{-2}) parts, which is tight up to the implied constant and solves a problem studied by Lovász and Szegedy. Expand
A new graph decomposition method for bipartite graphs
Given a sufficiently large and sufficiently dense bipartite graph G = (A,B;E), we present a novel method for decomposing the majority of the edges of G into quasirandom graphs so that the vertex setsExpand
Triangles in C5‐free graphs and hypergraphs of girth six
We introduce a new approach and prove that the maximum number of triangles in a $C_5$-free graph on $n$ vertices is at most $$(1 + o(1)) \frac{1}{3 \sqrt 2} n^{3/2}.$$ We also show a connection toExpand
A note on the maximum number of triangles in a C5-free graph
We prove that the maximum number of triangles in a C5-free graph on n vertices is at most [Formula presented](1+o(1))n3/2, improving an estimate of Alon and Shikhelman [Alon, N. and C. Shikhelman,Expand
A blow-up lemma for approximate decompositions
<p>We develop a new method for constructing approximate decompositions of dense graphs into sparse graphs and apply it to long-standing decomposition problems. For instance, our results imply theExpand
Resolution of the Oberwolfach problem
The Oberwolfach problem, posed by Ringel in 1967, asks for a decomposition of $K_{2n+1}$ into edge-disjoint copies of a given $2$-factor. We show that this can be achieved for all large $n$. WeExpand
...
1
2
3
...