A Substructure based Lower Bound for Eternal Vertex Cover Number

2021 ◽  
Author(s):  
Jasine Babu ◽  
Veena Prabhakaran ◽  
Arko Sharma
Keyword(s):  
Lower Bound ◽  
Vertex Cover

An Exact Algorithm for Minimum Vertex Cover Problem

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 603
Author(s):  
Luzhi Wang ◽  
Shuli Hu ◽  
Mingyang Li ◽  
Junping Zhou
Keyword(s):  
Lower Bound ◽  
Branch And Bound ◽  
Heuristic Algorithms ◽  
Vertex Cover ◽  
Exact Algorithm ◽  
Search Space ◽  
Exact Algorithms ◽  
The Other ◽  
Branch And Bound Algorithm ◽  
Cover Problem

In this paper, we propose a branch-and-bound algorithm to solve exactly the minimum vertex cover (MVC) problem. Since a tight lower bound for MVC has a significant influence on the efficiency of a branch-and-bound algorithm, we define two novel lower bounds to help prune the search space. One is based on the degree of vertices, and the other is based on MaxSAT reasoning. The experiment confirms that our algorithm is faster than previous exact algorithms and can find better results than heuristic algorithms.

scholarly journals Fractional Biclique Covers and Partitions of Graphs

10.37236/1100 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Valerie L. Watts
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Vertex Cover ◽  
Binary Matrix ◽  
Partition Number ◽  
Bipartite Subgraph ◽  
The Matrix ◽  
Boolean Rank ◽  
Complete Bipartite Subgraph

A biclique is a complete bipartite subgraph of a graph. This paper investigates the fractional biclique cover number, $bc^*(G)$, and the fractional biclique partition number, $bp^*(G)$, of a graph $G$. It is observed that $bc^*(G)$ and $bp^*(G)$ provide lower bounds on the biclique cover and partition numbers respectively, and conditions for equality are given. It is also shown that $bc^*(G)$ is a better lower bound on the Boolean rank of a binary matrix than the maximum number of isolated ones of the matrix. In addition, it is noted that $bc^*(G) \leq bp^*(G) \leq \beta^*(G)$, the fractional vertex cover number. Finally, the application of $bc^*(G)$ and $bp^*(G)$ to two different weak products is discussed.

Complexity of the Maximum k-Path Vertex Cover Problem

2020 ◽  
Vol E103.A (10) ◽  
pp. 1193-1201
Author(s):  
Eiji MIYANO ◽  
Toshiki SAITOH ◽  
Ryuhei UEHARA ◽  
Tsuyoshi YAGITA ◽  
Tom C. van der ZANDEN
Keyword(s):  
Vertex Cover ◽  
Vertex Cover Problem ◽  
Cover Problem

The least distance between extremums and minimal period of solutions to autonomous vector differential equations

2019 ◽  
Vol 485 (2) ◽  
pp. 142-144
Author(s):  
A. A. Zevin
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Lipschitz Constant ◽  
Minimal Period ◽  
Arbitrary Vector ◽  
Vector Norm ◽  
Sharp Lower Bound

Solutions x(t) of the Lipschitz equation x = f(x) with an arbitrary vector norm are considered. It is proved that the sharp lower bound for the distances between successive extremums of xk(t) equals π/L where L is the Lipschitz constant. For non-constant periodic solutions, the lower bound for the periods is 2π/L. These estimates are achieved for norms that are invariant with respect to permutation of the indices.

A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

10.37236/1188 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ramsey Numbers

For $k \geq 5$, we establish new lower bounds on the Schur numbers $S(k)$ and on the k-color Ramsey numbers of $K_3$.

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