Hypergraph families with bounded edge cover or transversal number

COMBINATORICA ◽  
1983 ◽  
Vol 3 (3-4) ◽  
pp. 351-358 ◽  
Author(s):  
A. Gyárfás ◽  
J. Lehel
Keyword(s):  
Edge Cover ◽  
Transversal Number

A note on improved upper bounds on the transversal number of hypergraphs

2019 ◽  
Vol 11 (01) ◽  
pp. 1950004
Author(s):  
Michael A. Henning ◽  
Nader Jafari Rad
Keyword(s):  
Upper Bound ◽  
Dominating Set ◽  
Domination Number ◽  
Minimum Size ◽  
Total Domination ◽  
Total Domination Number ◽  
Minimum Cardinality ◽  
Total Dominating Set ◽  
Isolated Vertex ◽  
Transversal Number

A subset [Formula: see text] of vertices in a hypergraph [Formula: see text] is a transversal if [Formula: see text] has a nonempty intersection with every edge of [Formula: see text]. The transversal number of [Formula: see text] is the minimum size of a transversal in [Formula: see text]. A subset [Formula: see text] of vertices in a graph [Formula: see text] with no isolated vertex, is a total dominating set if every vertex of [Formula: see text] is adjacent to a vertex of [Formula: see text]. The minimum cardinality of a total dominating set in [Formula: see text] is the total domination number of [Formula: see text]. In this paper, we obtain a new (improved) probabilistic upper bound for the transversal number of a hypergraph, and a new (improved) probabilistic upper bound for the total domination number of a graph.

On the Complexity of the Upper r-Tolerant Edge Cover Problem

2020 ◽  
pp. 32-47
Author(s):  
Ararat Harutyunyan ◽  
Mehdi Khosravian Ghadikolaei ◽  
Nikolaos Melissinos ◽  
Jérôme Monnot ◽  
Aris Pagourtzis
Keyword(s):  
Edge Cover ◽  
Cover Problem

scholarly journals Community Structure of Gastrpods in Mokupa Beach, Sub-district of Tobariri,Minahasa Regency, North Sulawesi Province

2015 ◽  
Vol 3 (1) ◽  
pp. 22
Author(s):  
Alinaung F. Firgonitha ◽  
Anneke V. Lohoo ◽  
Alex D. Kambey
Keyword(s):  
Diversity Index ◽  
High Tide ◽  
Ocean Basin ◽  
Food Chains ◽  
Seagrass Bed ◽  
Species Diversity Index ◽  
Tropical Ecosystem ◽  
Filter Feeder ◽  
Edge Cover ◽  
North Sulawesi

Ecologically intertidal mollusk has important role in the food chains. As a filter feeder, mollusk is also known as a food source for other marine organisms. The intertidal zone is known as the smallest area in the ocean basin (Nybakken, 1992). This zone is a narrow edge cover only few square meters and position between low tide mark (LTM) and high tide mark (HTM). The study was conducted in Mokupa beach waters, Tombariri sub-district, Minahasa Regency. Coastal area of Mokupa village represent typical tropical ecosystem such as coral reef, seagrass bed and mangrove belt. As many as 45 species in 134 total individuals were recorded during the study. The density of gastropods collected is 4.4667 individual/m2 while density for gastropods species Littoraria scabra Linne was 0.4000 individual/m2 and in term of relative density is 9.834 % and thus considered the highest. Species diversity index of this species is H’ = 2.37594. Keywords: mollusk, diversity, dominance   A B S T R A K   Secara ekologis Moluska yang menempati daerah intertidal memiliki peranan yang besar kaitannya dengan rantai makanan. Karena di samping sebagai filter feeder, moluska juga merupakan makanan bagi biota lainnya. Zona intertidal (pasang-surut) merupakan daerah terkecil dari semua daerah yang terdapat di samudera dunia (Nybakken, 1992). Zona ini merupakan pinggiran yang sempit sekali, hanya beberapa meter luasnya, terletak di antara air pasang tinggi dan air surut rendah. Penelitian ini dilaksanakan di perairan pantai Mokupa Kecamatan Tombariri Kabupaten Minahasa. Daerah pantai Desa Mokupa merupakan daerah yang lokasinya terdapat ekosistem yang khas di daerah tropis yaitu terumbu karang, padang lamun, dan hutan mangrove. Diperoleh sebanyak 45 spesies dan berjumlah 134 individu. Kepadatan rata-rata organisme Gastropoda diperoleh 4,4667 indv/m2 , dengan  kepadatan spesies tertinggi 0,4000 indv/m2 (Littoraria scabra Linne), dengan Kepadatan relative  adalah 9,834 %.Keanekaragaman spesies diperoleh nilai (H’= 2.37594)   Kata Kunci : Komunitas, keanekaragaman, dominasi 1Mahasiswa Program Studi MSP FPIK-UNSRAT 2Staf pengajar Fakultas Perikanan dan Ilmu Kelautan Universitas Sam Ratulangi

scholarly journals Greedy Random Walk

2013 ◽  
Vol 23 (2) ◽  
pp. 269-289 ◽  
Author(s):  
TAL ORENSHTEIN ◽  
IGOR SHINKAR
Keyword(s):  
Random Walk ◽  
Random Process ◽  
Discrete Time ◽  
Complete Graph ◽  
Cover Time ◽  
Edge Cover ◽  
Adjacent Edge ◽  
Natural Families

We study a discrete time self-interacting random process on graphs, which we call greedy random walk. The walker is located initially at some vertex. As time evolves, each vertex maintains the set of adjacent edges touching it that have not yet been crossed by the walker. At each step, the walker, being at some vertex, picks an adjacent edge among the edges that have not traversed thus far according to some (deterministic or randomized) rule. If all the adjacent edges have already been traversed, then an adjacent edge is chosen uniformly at random. After picking an edge the walker jumps along it to the neighbouring vertex. We show that the expected edge cover time of the greedy random walk is linear in the number of edges for certain natural families of graphs. Examples of such graphs include the complete graph, even degree expanders of logarithmic girth, and the hypercube graph. We also show that GRW is transient in$\mathbb{Z}^d$for alld≥ 3.

scholarly journals Approximation algorithms in combinatorial scientific computing

Acta Numerica ◽  
2019 ◽  
Vol 28 ◽  
pp. 541-633 ◽  
Author(s):  
Alex Pothen ◽  
S. M. Ferdous ◽  
Fredrik Manne
Keyword(s):  
Approximation Algorithms ◽  
Scientific Computing ◽  
Linear Time ◽  
Exact Algorithms ◽  
Edge Cover ◽  
Weighted Matching ◽  
Practical Algorithms ◽  
Modern Computer ◽  
Massive Graphs ◽  
Multiple Threads

We survey recent work on approximation algorithms for computing degree-constrained subgraphs in graphs and their applications in combinatorial scientific computing. The problems we consider include maximization versions of cardinality matching, edge-weighted matching, vertex-weighted matching and edge-weighted $b$-matching, and minimization versions of weighted edge cover and $b$-edge cover. Exact algorithms for these problems are impractical for massive graphs with several millions of edges. For each problem we discuss theoretical foundations, the design of several linear or near-linear time approximation algorithms, their implementations on serial and parallel computers, and applications. Our focus is on practical algorithms that yield good performance on modern computer architectures with multiple threads and interconnected processors. We also include information about the software available for these problems.

scholarly journals On the parameterized complexity of vertex cover and edge cover with connectivity constraints

2015 ◽  
Vol 565 ◽  
pp. 1-15 ◽  
Author(s):  
Henning Fernau ◽  
Fedor V. Fomin ◽  
Geevarghese Philip ◽  
Saket Saurabh
Keyword(s):  
Parameterized Complexity ◽  
Vertex Cover ◽  
Edge Cover

scholarly journals Hypergraphs with large transversal number

2013 ◽  
Vol 313 (8) ◽  
pp. 959-966 ◽  
Author(s):  
Michael A. Henning ◽  
Anders Yeo
Keyword(s):  
Transversal Number
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