scholarly journals On the Fractional Covering Number of Hypergraphs

1988 ◽  
Vol 1 (1) ◽  
pp. 45-49 ◽  
Author(s):  
F. R. K. Chung ◽  
Z. Füredi ◽  
M. R. Garey ◽  
R. L. Graham
Keyword(s):  
Covering Number ◽  
Fractional Covering

scholarly journals Uniform intersecting families with covering number four

1995 ◽  
Vol 71 (1) ◽  
pp. 127-145 ◽  
Author(s):  
Peter Frankl ◽  
Katsuhiro Ota ◽  
Norihide Tokushige
Keyword(s):  
Covering Number ◽  
Intersecting Families

scholarly journals The geodetic vertex covering number of a graph

2020 ◽  
Vol 8 (2) ◽  
pp. 683-689
Author(s):  
V.M. Arul Flower Mary ◽  
J. Anne Mary Leema ◽  
P. Titus ◽  
B. Uma Devi
Keyword(s):  
Covering Number ◽  
Vertex Covering

scholarly journals Cubical coloring — fractional covering by cuts and semidefinite programming

2015 ◽  
Vol Vol. 17 no.2 (Graph Theory) ◽  
Author(s):  
Robert Šámal
Keyword(s):  
Semidefinite Programming ◽  
Chromatic Number ◽  
Fractional Chromatic Number ◽  
Maximum Cut ◽  
Continuous Mappings ◽  
Polynomial Time Approximation Algorithm ◽  
Eigenvalue Bound ◽  
International Audience ◽  
Graph Parameters ◽  
Fractional Covering

International audience We introduce a new graph parameter that measures fractional covering of a graph by cuts. Besides being interesting in its own right, it is useful for study of homomorphisms and tension-continuous mappings. We study the relations with chromatic number, bipartite density, and other graph parameters. We find the value of our parameter for a family of graphs based on hypercubes. These graphs play for our parameter the role that cliques play for the chromatic number and Kneser graphs for the fractional chromatic number. The fact that the defined parameter attains on these graphs the correct value suggests that our definition is a natural one. In the proof we use the eigenvalue bound for maximum cut and a recent result of Engström, Färnqvist, Jonsson, and Thapper [An approximability-related parameter on graphs – properties and applications, DMTCS vol. 17:1, 2015, 33–66]. We also provide a polynomial time approximation algorithm based on semidefinite programming and in particular on vector chromatic number (defined by Karger, Motwani and Sudan [Approximate graph coloring by semidefinite programming, J. ACM 45 (1998), no. 2, 246–265]).

scholarly journals Investigating Numeric Relationships Using an Interactive Tool: Covering Number Sense Concepts for the Middle Grades

2010 ◽  
Vol 01 (02) ◽  
pp. 121-127
Author(s):  
Hui Fang Huang “Angie” Su ◽  
Carol A. Marinas ◽  
Joseph M. Furner
Keyword(s):  
Middle Grades ◽  
Number Sense ◽  
Covering Number ◽  
Interactive Tool

scholarly journals Characterization of asymmetric CKI- and KP-digraphs with covering number at most 3

2013 ◽  
Vol 313 (13) ◽  
pp. 1464-1474 ◽  
Author(s):  
Hortensia Galeana-Sánchez ◽  
Mika Olsen
Keyword(s):  
Covering Number

scholarly journals Graphs whose acyclic graphoidal covering number is one less than its maximum degree

2001 ◽  
Vol 240 (1-3) ◽  
pp. 231-237 ◽  
Author(s):  
S. Arumugam ◽  
I. Rajasingh ◽  
P.R.L. Pushpam
Keyword(s):  
Maximum Degree ◽  
Covering Number

On the multifractal analysis of the covering number on the Galton–Watson tree

2019 ◽  
Vol 56 (01) ◽  
pp. 265-281
Author(s):  
Najmeddine Attia
Keyword(s):  
Hausdorff Dimension ◽  
Multifractal Analysis ◽  
Covering Number

AbstractWe consider, for t in the boundary of a Galton–Watson tree $(\partial \textsf{T})$, the covering number $(\textsf{N}_n(t))$ by the generation-n cylinder. For a suitable set I and sequence (sn), we almost surely establish the Hausdorff dimension of the set $\{ t \in \partial {\textsf{T}}:{{\textsf{N}}_n}(t) - nb \ {\sim} \ {s_n}\} $ for b ∈ I.

scholarly journals On the König deficiency of zero-reducible graphs

2019 ◽  
Vol 39 (1) ◽  
pp. 273-292
Author(s):  
Miklós Bartha ◽  
Miklós Krész
Keyword(s):  
Perfect Matching ◽  
Linear Time ◽  
Perfect Matchings ◽  
Covering Number ◽  
Matching Number ◽  
Empty Graph ◽  
Reduction System ◽  
Vertex Covering ◽  
Np Complete ◽  
The Difference

Abstract A confluent and terminating reduction system is introduced for graphs, which preserves the number of their perfect matchings. A union-find algorithm is presented to carry out reduction in almost linear time. The König property is investigated in the context of reduction by introducing the König deficiency of a graph G as the difference between the vertex covering number and the matching number of G. It is shown that the problem of finding the König deficiency of a graph is NP-complete even if we know that the graph reduces to the empty graph. Finally, the König deficiency of graphs G having a vertex v such that $$G-v$$G-v has a unique perfect matching is studied in connection with reduction.

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