scholarly journals Finding and counting cliques and independent sets in r-uniform hypergraphs

2006 ◽  
Vol 99 (4) ◽  
pp. 130-134 ◽  
Author(s):  
Raphael Yuster
Keyword(s):  
Independent Sets ◽  
Uniform Hypergraphs

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

Trees without twin-leaves with smallest number of maximal independent sets

2020 ◽  
Vol 30 (1) ◽  
pp. 53-67 ◽  
Author(s):  
Dmitriy S. Taletskii ◽  
Dmitriy S. Malyshev
Keyword(s):  
Independent Sets ◽  
Adjacent Vertex ◽  
Maximal Independent Sets

AbstractFor any n, in the set of n-vertex trees such that any two leaves have no common adjacent vertex, we describe the trees with the smallest number of maximal independent sets.

scholarly journals Rainbow matchings for 3-uniform hypergraphs

2021 ◽  
Vol 183 ◽  
pp. 105489
Author(s):  
Hongliang Lu ◽  
Xingxing Yu ◽  
Xiaofan Yuan
Keyword(s):  
Uniform Hypergraphs

scholarly journals Covering Small Independent Sets and Separators with Applications to Parameterized Algorithms

2020 ◽  
Vol 16 (3) ◽  
pp. 1-31
Author(s):  
Daniel Lokshtanov ◽  
Fahad Panolan ◽  
Saket Saurabh ◽  
Roohani Sharma ◽  
Meirav Zehavi
Keyword(s):  
Independent Sets ◽  
Parameterized Algorithms

scholarly journals Hypercycle Systems of 5-Cycles in Complete 3-Uniform Hypergraphs

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 484
Author(s):  
Anita Keszler ◽  
Zsolt Tuza
Keyword(s):  
Element Subset ◽  
Uniform Hypergraphs ◽  
Vertex Set ◽  
Recursive Constructions

In this paper, we consider the problem of constructing hypercycle systems of 5-cycles in complete 3-uniform hypergraphs. A hypercycle system C(r,k,v) of order v is a collection of r-uniform k-cycles on a v-element vertex set, such that each r-element subset is an edge in precisely one of those k-cycles. We present cyclic hypercycle systems C(3,5,v) of orders v=25,26,31,35,37,41,46,47,55,56, a highly symmetric construction for v=40, and cyclic 2-split constructions of orders 32,40,50,52. As a consequence, all orders v≤60 permitted by the divisibility conditions admit a C(3,5,v) system. New recursive constructions are also introduced.

Independent sets in n-vertex k-chromatic ℓ-connected graphs

2021 ◽  
Vol 344 (7) ◽  
pp. 112376
Author(s):  
John Engbers ◽  
Lauren Keough ◽  
Taylor Short
Keyword(s):  
Independent Sets ◽  
Connected Graphs

scholarly journals Coincidence counter measurements of cosmic rays in an aeroplane

1936 ◽  
Vol 156 (889) ◽  
pp. 570-577 ◽  
Keyword(s):  
Cosmic Rays ◽  
High Altitude ◽  
Cosmic Ray ◽  
Independent Sets ◽  
Vertical Line ◽  
Coincidence Counting ◽  
Detailed Design ◽  
Recording Apparatus ◽  
Coincidence Counter ◽  
Balloon Experiments

Cosmic ray measurements on mountains are limited in general to altitudes below about 4000 meters. Above this height Regener has made successful use of small balloons carrying self-recording apparatus, and occasional flights have been made with manned balloons by Piccard, Cosyns, and by American workers. Balloon experiments are, however, hardly practicable in this country, so we decided to investigate cosmic rays, and in particular the production of showers, using an aeroplane. Facilities for flying to a height of about 10 km. Were generously provided by the Air Ministry. Apparatus Two independent sets of three tube counters were used in conjunction with the usual coincidence counting circuits. The counters could be arranged in a vertical line to record vertical penetrating particles, or in a triangle to record showers. The triple coincidences were recorded by telephone counters which were photographed at intervals together with a clock and aneroid barometer. The detailed design of the apparatus required some consideration since the aeroplane available (the Vickers Vespa machine used for high altitude experiments at the Royal Aircraft Establishment) had an open observer’s cockpit in which the counting set had to be installed.

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