scholarly journals The existence of path-factor covered graphs

2020 ◽  
Author(s):  
Guowei Dai
Keyword(s):  
Path Factor

Some results about component factors in graphs

2019 ◽  
Vol 53 (3) ◽  
pp. 723-730 ◽  
Author(s):  
Sizhong Zhou
Keyword(s):  
Positive Integer ◽  
Connected Graph ◽  
Connected Graphs ◽  
Spanning Subgraph ◽  
Component Factor ◽  
Path Factor

For a set ℋ of connected graphs, a spanning subgraph H of a graph G is called an ℋ-factor of G if every component of H is isomorphic to a member ofℋ. An H-factor is also referred as a component factor. If each component of H is a star (resp. path), H is called a star (resp. path) factor. By a P≥ k-factor (k positive integer) we mean a path factor in which each component path has at least k vertices (i.e. it has length at least k − 1). A graph G is called a P≥ k-factor covered graph, if for each edge e of G, there is a P≥ k-factor covering e. In this paper, we prove that (1) a graph G has a {K1,1,K1,2, … ,K1,k}-factor if and only if bind(G) ≥ 1/k, where k ≥ 2 is an integer; (2) a connected graph G is a P≥ 2-factor covered graph if bind(G) > 2/3; (3) a connected graph G is a P≥ 3-factor covered graph if bind(G) ≥ 3/2. Furthermore, it is shown that the results in this paper are best possible in some sense.

scholarly journals Sufficient conditions for the existence of a path-factor which are related to odd components

2018 ◽  
Vol 89 (3) ◽  
pp. 327-340 ◽  
Author(s):  
Yoshimi Egawa ◽  
Michitaka Furuya ◽  
Kenta Ozeki
Keyword(s):  
Sufficient Conditions ◽  
Path Factor

scholarly journals Sun Toughness Conditions for P 2 and P 3 Factor Uniform and Factor Critical Avoidable Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Shu Gong ◽  
Haci Mehmet Baskonus ◽  
Wei Gao
Keyword(s):  
Graph Theory ◽  
Computer Networks ◽  
The Sun ◽  
Graph Structure ◽  
Network Graph ◽  
The Given ◽  
Path Factor

The security of a network is closely related to the structure of the network graph. The denser the network graph structure is, the better it can resist attacks. Toughness and isolated toughness are used to characterize the vulnerable programs of the network which have been paid attention from mathematics and computer scholars. On this basis, considering the particularity of the sun component structures, sun toughness was introduced in mathematics and applied to computer networks. From the perspective of modern graph theory, this paper presents the sun toughness conditions of the path factor uniform graph and the path factor critical avoidable graph in P ≥ 2 -factor and P ≥ 3 -factor settings. Furthermore, examples show that the given boundaries are sharp.

scholarly journals Isolated toughness and path-factor uniform graphs

2021 ◽  
Author(s):  
Sizhong Zhou ◽  
Zhiren Sun ◽  
Hongxia Liu
Keyword(s):  
Connected Graph ◽  
Edge Connectivity ◽  
Spanning Subgraph ◽  
K Factor ◽  
Path Factor

A $P_{\geq k}$-factor of a graph $G$ is a spanning subgraph of $G$ whose components are paths of order at least $k$. We say that a graph $G$ is $P_{\geq k}$-factor covered if for every edge $e\in E(G)$, $G$ admits a $P_{\geq k}$-factor that contains $e$; and we say that a graph $G$ is $P_{\geq k}$-factor uniform if for every edge $e\in E(G)$, the graph $G-e$ is $P_{\geq k}$-factor covered. In other words, $G$ is $P_{\geq k}$-factor uniform if for every pair of edges $e_1,e_2\in E(G)$, $G$ admits a $P_{\geq k}$-factor that contains $e_1$ and avoids $e_2$. In this article, we testify that (\romannumeral1) a 3-edge-connected graph $G$ is $P_{\geq2}$-factor uniform if its isolated toughness $I(G)>1$; (\romannumeral2) a 3-edge-connected graph $G$ is $P_{\geq3}$-factor uniform if its isolated toughness $I(G)>2$. Furthermore, we explain that these conditions on isolated toughness and edge-connectivity in our main results are best possible in some sense.

scholarly journals The Existence of a Path-Factor without Small Odd Paths

10.37236/5817 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Yoshimi Egawa ◽  
Michitaka Furuya
Keyword(s):  
Number Of Components ◽  
Spanning Subgraph ◽  
Path Factor

A $\{P_{2},P_{5}\}$-factor of a graph is a spanning subgraph of the graph each of whose components is isomorphic to either $P_{2}$ or $P_{5}$, where $P_{n}$ denote the path of order $n$. In this paper, we show that if a graph $G$ satisfies $c_{1}(G-X)+\frac{2}{3}c_{3}(G-X)\leq \frac{4}{3}|X|+\frac{1}{3}$ for all $X\subseteq V(G)$, then $G$ has a $\{P_{2},P_{5}\}$-factor, where $c_{i}(G-X)$ is the number of components $C$ of $G-X$ with $|V(C)|=i$. Moreover, it is shown that above condition is sharp.

scholarly journals How do firms adjust production factors to the cycle?

2016 ◽  
Vol 16 (2) ◽  
Author(s):  
Gilbert Cette ◽  
Rémy Lecat ◽  
Ahmed Ould Ahmed Jiddou
Keyword(s):  
Capital Stock ◽  
Operating Time ◽  
Capacity Utilization ◽  
Working Time ◽  
Production Factors ◽  
Multiple Dimensions ◽  
Time Offset ◽  
The Impact ◽  
Time Lead ◽  
Path Factor

AbstractThis paper studies the adjustment of production factors to the cycle taking into account factor utilization in multiple dimensions (labor working time, capital operating time and capital capacity utilization) and examines the impact of obstacles to increasing capital operating time on this adjustment path. Factor utilization adjusts the most rapidly, first through capital capacity utilization and capital operating time and then labor working time. The adjustment is slow for the number of employees and even slower for the capital stock. Obstacles to increasing capital operating time lead to a slower adjustment of capital operating time, offset by a stronger adjustment of capacity utilization.

scholarly journals NSRD-10: Leak Path Factor Guidance Using MELCOR

2017 ◽  
Author(s):  
David Louie ◽  
Larry L. Humphries
Keyword(s):  
Path Factor
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