Hypergraphs with large transversal number and with edge sizes at least 3

2008 ◽  
pp. n/a-n/a
Author(s):  
Michael A. Henning ◽  
Anders Yeo
Keyword(s):  
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.

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

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

scholarly journals The clique-transversal number of a{K1,3,K4}-free 4-regular graph

2015 ◽  
Vol 338 (7) ◽  
pp. 1126-1130
Author(s):  
Fenling Xu ◽  
Baoyindureng Wu ◽  
Qinqin Li
Keyword(s):  
Regular Graph ◽  
Transversal Number

Bounds on the clique-transversal number of regular graphs

2008 ◽  
Vol 51 (5) ◽  
pp. 851-863 ◽  
Author(s):  
ErFang Shan ◽  
T. C. E. Cheng ◽  
LiYing Kang
Keyword(s):  
Regular Graphs ◽  
Transversal Number

scholarly journals Claw-free cubic graphs with clique-transversal number half of their order

2011 ◽  
Vol 24 (7) ◽  
pp. 1080-1083
Author(s):  
Erfang Shan ◽  
Haichao Wang
Keyword(s):  
Cubic Graphs ◽  
Transversal Number

Hypergraphs with large transversal number and with edge sizes at least four

2012 ◽  
Vol 10 (3) ◽  
pp. 1133-1140 ◽  
Author(s):  
Michael A. Henning ◽  
Christian Löwenstein
Keyword(s):  
Transversal Number
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