scholarly journals Randomized greedy algorithm for independent sets in regular uniform hypergraphs with large girth

2021 ◽  
Author(s):  
Jiaxi Nie ◽  
Jacques Verstraëte
Keyword(s):  
Greedy Algorithm ◽  
Independent Sets ◽  
Uniform Hypergraphs ◽  
Large Girth

Approximating Coloring and Maximum Independent Sets in 3-Uniform Hypergraphs

2001 ◽  
Vol 41 (1) ◽  
pp. 99-113 ◽  
Author(s):  
Michael Krivelevich ◽  
Ram Nathaniel ◽  
Benny Sudakov
Keyword(s):  
Independent Sets ◽  
Uniform Hypergraphs

scholarly journals Computing independent sets in graphs with large girth

1992 ◽  
Vol 35 (2) ◽  
pp. 167-170 ◽  
Author(s):  
Owen J. Murphy
Keyword(s):  
Independent Sets ◽  
Large Girth

A note on the Greedy algorithm for finding independent sets of -free graphs

2009 ◽  
Vol 109 (10) ◽  
pp. 485-489
Author(s):  
Ippei Koura ◽  
Takao Ono ◽  
Tomio Hirata
Keyword(s):  
Greedy Algorithm ◽  
Independent Sets ◽  
The Greedy Algorithm

Colorings of uniform hypergraphs with large girth

2012 ◽  
Vol 85 (2) ◽  
pp. 247-250 ◽  
Author(s):  
A. B. Kupavskii ◽  
D. A. Shabanov
Keyword(s):  
Uniform Hypergraphs ◽  
Large Girth

Locally Dense Independent Sets in Regular Graphs of Large Girth—An Example of a New Approach

2008 ◽  
pp. 163-183 ◽  
Author(s):  
Frank Göring ◽  
Jochen Harant ◽  
Dieter Rautenbach ◽  
Ingo Schiermeyer
Keyword(s):  
Independent Sets ◽  
Regular Graphs ◽  
New Approach ◽  
Large Girth

Colourings of Uniform Hypergraphs with Large Girth and Applications

2017 ◽  
Vol 27 (2) ◽  
pp. 245-273 ◽  
Author(s):  
ANDREY KUPAVSKII ◽  
DMITRY SHABANOV
Keyword(s):  
Lower Bound ◽  
Arithmetic Progression ◽  
Absolute Constant ◽  
Combinatorial Problem ◽  
Uniform Hypergraphs ◽  
Probabilistic Technique ◽  
Formula Group ◽  
Large Girth ◽  
Image Position

This paper deals with a combinatorial problem concerning colourings of uniform hypergraphs with large girth. We prove that ifHis ann-uniform non-r-colourable simple hypergraph then its maximum edge degree Δ(H) satisfies the inequality$$ \Delta(H)\geqslant c\cdot r^{n-1}\ffrac{n(\ln\ln n)^2}{\ln n} $$for some absolute constantc> 0.As an application of our probabilistic technique we establish a lower bound for the classical van der Waerden numberW(n, r), the minimum naturalNsuch that in an arbitrary colouring of the set of integers {1,. . .,N} withrcolours there exists a monochromatic arithmetic progression of lengthn. We prove that$$ W(n,r)\geqslant c\cdot r^{n-1}\ffrac{(\ln\ln n)^2}{\ln n}. $$

scholarly journals Randomized Greedy Algorithms for Independent Sets and Matchings in Regular Graphs: Exact Results and Finite Girth Corrections

2009 ◽  
Vol 19 (1) ◽  
pp. 61-85 ◽  
Author(s):  
DAVID GAMARNIK ◽  
DAVID A. GOLDBERG
Keyword(s):  
Greedy Algorithm ◽  
Greedy Algorithms ◽  
Independent Set ◽  
Independent Sets ◽  
Simple Expression ◽  
Regular Graphs ◽  
Bounded Degree ◽  
Constant Degree ◽  
Image Position ◽  
The Greedy Algorithm

We derive new results for the performance of a simple greedy algorithm for finding large independent sets and matchings in constant-degree regular graphs. We show that forr-regular graphs withnnodes and girth at leastg, the algorithm finds an independent set of expected cardinalitywheref(r) is a function which we explicitly compute. A similar result is established for matchings. Our results imply improved bounds for the size of the largest independent set in these graphs, and provide the first results of this type for matchings. As an implication we show that the greedy algorithm returns a nearly perfect matching when both the degreerand girthgare large. Furthermore, we show that the cardinality of independent sets and matchings produced by the greedy algorithm inarbitrarybounded-degree graphs is concentrated around the mean. Finally, we analyse the performance of the greedy algorithm for the case of random i.i.d. weighted independent sets and matchings, and obtain a remarkably simple expression for the limiting expected values produced by the algorithm. In fact, all the other results are obtained as straightforward corollaries from the results for the weighted case.

scholarly journals Invariant Gaussian processes and independent sets on regular graphs of large girth

2014 ◽  
Vol 47 (2) ◽  
pp. 284-303 ◽  
Author(s):  
Endre Csóka ◽  
Balázs Gerencsér ◽  
Viktor Harangi ◽  
Bálint Virág
Keyword(s):  
Gaussian Processes ◽  
Independent Sets ◽  
Regular Graphs ◽  
Large Girth
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