On degree sum conditions for directed path-factors with a specified number of paths

2020 ◽  
Vol 343 (12) ◽  
pp. 112114
Author(s):  
Shuya Chiba ◽  
Eishi Mishio ◽  
Pierre Montalbano
Keyword(s):  
Directed Path ◽  
Degree Sum

scholarly journals Degree and neighborhood intersection conditions restricted to induced subgraphs ensuring Hamiltonicity of graphs

2014 ◽  
Vol 06 (03) ◽  
pp. 1450043
Author(s):  
Bo Ning ◽  
Shenggui Zhang ◽  
Bing Chen
Keyword(s):  
Hamilton Cycles ◽  
Induced Subgraphs ◽  
Degree Sum ◽  
Degree Condition

Let claw be the graph K1,3. A graph G on n ≥ 3 vertices is called o-heavy if each induced claw of G has a pair of end-vertices with degree sum at least n, and called 1-heavy if at least one end-vertex of each induced claw of G has degree at least n/2. In this note, we show that every 2-connected o-heavy or 3-connected 1-heavy graph is Hamiltonian if we restrict Fan-type degree condition or neighborhood intersection condition to certain pairs of vertices in some small induced subgraphs of the graph. Our results improve or extend previous results of Broersma et al., Chen et al., Fan, Goodman and Hedetniemi, Gould and Jacobson, and Shi on the existence of Hamilton cycles in graphs.

scholarly journals Nonhamiltonian 2-connected claw-free graphs with large 4-degree sum

2001 ◽  
Vol 236 (1-3) ◽  
pp. 123-130 ◽  
Author(s):  
Wacław Frydrych
Keyword(s):  
Degree Sum

scholarly journals Degree sum conditions for the circumference of 4-connected graphs

2014 ◽  
Vol 333 ◽  
pp. 66-83
Author(s):  
Shuya Chiba ◽  
Masao Tsugaki ◽  
Tomoki Yamashita
Keyword(s):  
Connected Graphs ◽  
Degree Sum

GENERA OF THE LINKS DERIVED FROM 2-CONNECTED PLANE GRAPHS

2012 ◽  
Vol 21 (14) ◽  
pp. 1250129 ◽  
Author(s):  
SHUYA LIU ◽  
HEPING ZHANG
Keyword(s):  
Explicit Formula ◽  
Large Family ◽  
Plane Graph ◽  
Plane Graphs ◽  
Degree Sum ◽  
Oriented Link

In this paper, we associate a plane graph G with an oriented link by replacing each vertex of G with a special oriented n-tangle diagram. It is shown that such an oriented link has the minimum genus over all orientations of its unoriented version if its associated plane graph G is 2-connected. As a result, the genera of a large family of unoriented links are determined by an explicit formula in terms of their component numbers and the degree sum of their associated plane graphs.

scholarly journals Controllability of Weighted and Directed Networks with Nonidentical Node Dynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Linying Xiang ◽  
Jonathan J. H. Zhu ◽  
Fei Chen ◽  
Guanrong Chen
Keyword(s):  
Graph Theory ◽  
Control Theory ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Directed Path ◽  
Directed Networks ◽  
Leaders And Followers ◽  
Heterogenous Network

The concept of controllability from control theory is applied to weighted and directed networks with heterogenous linear or linearized node dynamics subject to exogenous inputs, where the nodes are grouped into leaders and followers. Under this framework, the controllability of the controlled network can be decomposed into two independent problems: the controllability of the isolated leader subsystem and the controllability of the extended follower subsystem. Some necessary and/or sufficient conditions for the controllability of the leader-follower network are derived based on matrix theory and graph theory. In particular, it is shown that a single-leader network is controllable if it is a directed path or cycle, but it is uncontrollable for a complete digraph or a star digraph in general. Furthermore, some approaches to improving the controllability of a heterogenous network are presented. Some simulation examples are given for illustration and verification.

Some Results on Degree Sum Energy of a Graph

2020 ◽  
pp. 353-359
Author(s):  
Mitesh J. Patel ◽  
G. V. Ghodasara
Keyword(s):  
Degree Sum

On a Sharp Degree Sum Condition for Disjoint Chorded Cycles in Graphs

2010 ◽  
Vol 26 (2) ◽  
pp. 173-186 ◽  
Author(s):  
Shuya Chiba ◽  
Shinya Fujita ◽  
Yunshu Gao ◽  
Guojun Li
Keyword(s):  
Degree Sum ◽  
Chorded Cycles ◽  
Degree Sum Condition

scholarly journals p-box: a new graph model

2015 ◽  
Vol Vol. 17 no. 1 (Graph Theory) ◽  
Author(s):  
Mauricio Soto ◽  
Christopher Thraves-Caro
Keyword(s):  
Graph Theory ◽  
Graph Model ◽  
Directed Path ◽  
Outerplanar Graphs ◽  
New Model ◽  
Model Based ◽  
Representative Element ◽  
International Audience ◽  
Graph Families

Graph Theory International audience In this document, we study the scope of the following graph model: each vertex is assigned to a box in ℝd and to a representative element that belongs to that box. Two vertices are connected by an edge if and only if its respective boxes contain the opposite representative element. We focus our study on the case where boxes (and therefore representative elements) associated to vertices are spread in ℝ. We give both, a combinatorial and an intersection characterization of the model. Based on these characterizations, we determine graph families that contain the model (e. g., boxicity 2 graphs) and others that the new model contains (e. g., rooted directed path). We also study the particular case where each representative element is the center of its respective box. In this particular case, we provide constructive representations for interval, block and outerplanar graphs. Finally, we show that the general and the particular model are not equivalent by constructing a graph family that separates the two cases.

scholarly journals Fully Dynamic Transitive Closure in Plane Dags with one Source and one Sink

1994 ◽  
Vol 1 (30) ◽  
Author(s):  
Thore Husfeldt
Keyword(s):  
Transitive Closure ◽  
Upper Bounds ◽  
Directed Acyclic Graphs ◽  
Closure Problem ◽  
Directed Path ◽  
Lower And Upper Bounds ◽  
New Techniques ◽  
Time Dynamic ◽  
Acyclic Graphs ◽  
Closure Algorithm

We give an algorithm for the Dynamic Transitive Closure Problem for planar directed acyclic graphs with one source and one sink. The graph can be updated in logarithmic time under arbitrary edge insertions and deletions that preserve the embedding. Queries of the form `is there a directed path from u to v ?' for arbitrary vertices u and v can be answered in logarithmic time. The size of the data structure and the initialisation time are linear in the number of edges.<br /> <br />The result enlarges the class of graphs for which a logarithmic (or even polylogarithmic) time dynamic transitive closure algorithm exists. Previously, the only algorithms within the stated resource bounds put restrictions on the topology of the graph or on the delete operation. To obtain our result, we use a new characterisation of the transitive closure in plane graphs with one source and one sink and introduce new techniques to exploit this characterisation.<br /> <br />We also give a lower bound of Omega(log n/log log n) on the amortised complexity of the problem in the cell probe model with logarithmic word size. This is the first dynamic directed graph problem with almost matching lower and upper bounds.

Sign in / Sign up

Export Citation Format

Share Document