scholarly journals Algoritmos eficientes para emparelhamentos desconexos em grafos cordais e grafos bloco

2019 ◽  
Author(s):  
Bruno Masquio ◽  
Paulo Pinto ◽  
Jayme Szwarcfiter
Keyword(s):  
Graph Theory ◽  
Graph Matching ◽  
Efficient Algorithms ◽  
Chordal Graphs ◽  
Maximum Matching ◽  
Matching Problems ◽  
Block Graphs ◽  
Points Of View ◽  
Theoretical Characterization

Graph matching problems are well studied and bring great contributions to Graph Theory from both the theoretical and practical points of view. There are numerous studies for unrestricted and weighted/unweighted matchings. More recently, subgraph-restricted matchings have been proposed, which consider properties of the subgraph induced by the vertices of the matching. In this paper, we approach one of these new proposals, disconnected matching, which seeks to study maximum matching, such that the subgraph induced by the matching vertices is disconnected. We have described efficient algorithms to solve the problem for chordal graphs and block graphs based on a theoretical characterization.

scholarly journals Emparelhamentos Conexos

2020 ◽  
Author(s):  
Bruno P. Masquio ◽  
Paulo E. D. Pinto ◽  
Jayme L. Szwarcfiter
Keyword(s):  
Connected Graph ◽  
Graph Matching ◽  
Linear Time ◽  
Time Algorithm ◽  
Maximum Matching ◽  
Linear Time Algorithm ◽  
Induced Subgraphs ◽  
Matching Problems ◽  
General Graph ◽  
The One

Graph matching problems are well known and studied, in which we want to find sets of pairwise non-adjacent edges. Recently, there has been an interest in the study of matchings in which the induced subgraphs by the vertices of matchings are connected or disconnected. Although these problems are related to connectivity, the two problems are probably quite different, regarding their complexity. While the complexity of finding a maximum disconnected mat- ching is still unknown for a general graph, the one for connected matchings can be solved in polynomial time. Our contribution in this paper is a linear time algorithm to find a maximum connected matching of a general connected graph, given a general maximum matching as input.

scholarly journals On probe 2-clique graphs and probe diamond-free graphs

2015 ◽  
Vol Vol. 17 no. 1 (Graph Theory) ◽  
Author(s):  
Flavia Bonomo ◽  
Celina M. H. Figueiredo ◽  
Guillermo Duran ◽  
Luciano N. Grippo ◽  
Martín D. Safe ◽  
...  
Keyword(s):  
Graph Theory ◽  
Recognition Algorithm ◽  
Chordal Graphs ◽  
Stable Set ◽  
Induced Subgraphs ◽  
Forbidden Induced Subgraphs ◽  
Block Graphs ◽  
International Audience ◽  
Clique Graphs ◽  
Probe Block

Graph Theory International audience Given a class G of graphs, probe G graphs are defined as follows. A graph G is probe G if there exists a partition of its vertices into a set of probe vertices and a stable set of nonprobe vertices in such a way that non-edges of G, whose endpoints are nonprobe vertices, can be added so that the resulting graph belongs to G. We investigate probe 2-clique graphs and probe diamond-free graphs. For probe 2-clique graphs, we present a polynomial-time recognition algorithm. Probe diamond-free graphs are characterized by minimal forbidden induced subgraphs. As a by-product, it is proved that the class of probe block graphs is the intersection between the classes of chordal graphs and probe diamond-free graphs.

Framed 4-valent graph minor theory I: Introduction. A planarity criterion and linkless embeddability

2014 ◽  
Vol 23 (07) ◽  
pp. 1460002
Author(s):  
Vassily Olegovich Manturov
Keyword(s):  
Graph Theory ◽  
The Other ◽  
Graph Minor ◽  
Other Hand ◽  
Simple Class ◽  
Points Of View ◽  
General Graphs ◽  
Planarity Criterion

This paper is the first one in the sequence of papers about a simple class of framed 4-graphs; the goal of this paper is to collect some well-known results on planarity and to reformulate them in the language of minors. The goal of the whole sequence is to prove analogs of the Robertson–Seymour–Thomas theorems for framed 4-graphs: namely, we shall prove that many minor-closed properties are classified by finitely many excluded graphs. From many points of view, framed 4-graphs are easier to consider than general graphs; on the other hand, framed 4-graphs are closely related to many problems in graph theory.

CONNECTED LIAR'S DOMINATION IN GRAPHS: COMPLEXITY AND ALGORITHMS

2013 ◽  
Vol 05 (04) ◽  
pp. 1350024 ◽  
Author(s):  
B. S. PANDA ◽  
S. PAUL
Keyword(s):  
Dominating Set ◽  
Chordal Graphs ◽  
Hardness Of Approximation ◽  
Induced Subgraph ◽  
Path Graph ◽  
Block Graphs ◽  
Domination Problem ◽  
Np Complete ◽  
Domination In Graphs ◽  
General Graphs

A subset L ⊆ V of a graph G = (V, E) is called a connected liar's dominating set of G if (i) for all v ∈ V, |NG[v] ∩ L| ≥ 2, (ii) for every pair u, v ∈ V of distinct vertices, |(NG[u]∪NG[v])∩L| ≥ 3, and (iii) the induced subgraph of G on L is connected. In this paper, we initiate the algorithmic study of minimum connected liar's domination problem by showing that the corresponding decision version of the problem is NP-complete for general graph. Next we study this problem in subclasses of chordal graphs where we strengthen the NP-completeness of this problem for undirected path graph and prove that this problem is linearly solvable for block graphs. Finally, we propose an approximation algorithm for minimum connected liar's domination problem and investigate its hardness of approximation in general graphs.

Recognizing Topological Analogy in Semantic Network

2015 ◽  
Vol 24 (03) ◽  
pp. 1550006 ◽  
Author(s):  
Milan Trifunovic ◽  
Milos Stojkovic ◽  
Dragan Misic ◽  
Miroslav Trajanovic ◽  
Miodrag Manic
Keyword(s):  
Graph Matching ◽  
Semantic Network ◽  
Semantic Model ◽  
Input Graph ◽  
Matching Problems ◽  
Semantic Categorization ◽  
Maximum Common Subgraph ◽  
Oriented Structure ◽  
Node Labels

Recognizing topological analogy between the parts of semantic network seems to be very important step in the process of semantic categorization and interpretation of data that are embedded into the semantic network. Considering the semantic network as a set of graphs, recognition of topological analogy between the parts of semantic network can be treated as maximum common subgraph problem which falls in the group of exact graph matching problems. In this paper authors propose a new algorithm for maximum common subgraph detection aimed to a specific semantic network called Active Semantic Model (ASM). This semantic network can be represented as the set of labeled directed multigraphs with unique node labels. The structure of these graphs is specific because associations or edges are labeled with several attributes and some of them are related to nodes connected by edge. That kind of association-oriented structure enables associations or edges to play key role in the process of semantic categorization and interpretation of data. Furthermore, this kind of structure enables modeling semantic contexts in a form of semantically designated graphs (of associations). Proposed algorithm is capable of recognizing simultaneously maximum common subgraph of input graph and each of the graphs representing different contexts in ASM semantic network.

Quantitative Calculation Methods of Modules Matching for Product Configuration

2010 ◽  
Vol 20-23 ◽  
pp. 1391-1396
Author(s):  
Jie Hui Zou ◽  
Qun Gui Du
Keyword(s):  
Graph Theory ◽  
Design Method ◽  
Product Configuration ◽  
Calculation Methods ◽  
Matching Problems ◽  
Future Studies ◽  
Quantitative Calculation ◽  
Attribute Matching ◽  
Important Design

Modularization is an important design method cope with complicated and diversified products.Firstly, idea of quantitative calculation about modules matching base on attribute matching functions is proposed. Secondly, matching problems between two modules and among multi-modules are studied deeply by using graph theory. Then, a simple example is given to show the process of quantitative calculation and prove its feasibility. Finally, conclusions and future studies are presented.

scholarly journals On graphs with equal dominating and c-dominating energy

2019 ◽  
Vol 4 (2) ◽  
pp. 503-512 ◽  
Author(s):  
S. M. Hosamani ◽  
V. B. Awati ◽  
R. M. Honmore
Keyword(s):  
Graph Theory ◽  
Statistical Tools ◽  
Unicyclic Graphs ◽  
Mathematical Properties ◽  
Graph Energy ◽  
Block Graphs ◽  
Domination In Graphs

AbstractGraph energy and domination in graphs are most studied areas of graph theory. In this paper we try to connect these two areas of graph theory by introducing c-dominating energy of a graph G. First, we show the chemical applications of c-dominating energy with the help of well known statistical tools. Next, we obtain mathematical properties of c-dominating energy. Finally, we characterize trees, unicyclic graphs, cubic and block graphs with equal dominating and c-dominating energy.

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