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 A Linear Time Algorithm for a Variant of the MAX CUT Problem in Series Parallel Graphs

2017 ◽  
Vol 2017 ◽  
pp. 1-4 ◽  
Author(s):  
Brahim Chaourar
Keyword(s):  
Linear Time ◽  
Maximum Flow ◽  
Time Algorithm ◽  
Minimum Cut ◽  
Linear Time Algorithm ◽  
Induced Subgraphs ◽  
Positive Weight ◽  
Max Cut Problem ◽  
In Series ◽  
Minimum Cut Problem

Given a graph G=V,E, a connected sides cut U,V\U or δU is the set of edges of E linking all vertices of U to all vertices of V\U such that the induced subgraphs GU and GV\U are connected. Given a positive weight function w defined on E, the maximum connected sides cut problem (MAX CS CUT) is to find a connected sides cut Ω such that wΩ is maximum. MAX CS CUT is NP-hard. In this paper, we give a linear time algorithm to solve MAX CS CUT for series parallel graphs. We deduce a linear time algorithm for the minimum cut problem in the same class of graphs without computing the maximum flow.

scholarly journals The maximum weight spanning star forest problem on cactus graphs

2015 ◽  
Vol 07 (02) ◽  
pp. 1550018 ◽  
Author(s):  
Viet Hung Nguyen
Keyword(s):  
Connected Graph ◽  
Genomic Sequence ◽  
Linear Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Connected Component ◽  
Maximum Weight ◽  
Cactus Graphs ◽  
Np Hardness

A star is a graph in which some node is incident with every edge of the graph, i.e., a graph of diameter at most 2. A star forest is a graph in which each connected component is a star. Given a connected graph G in which the edges may be weighted positively. A spanning star forest of G is a subgraph of G which is a star forest spanning the nodes of G. The size of a spanning star forest F of G is defined to be the number of edges of F if G is unweighted and the total weight of all edges of F if G is weighted. We are interested in the problem of finding a Maximum Weight spanning Star Forest (MWSFP) in G. In [C. T. Nguyen, J. Shen, M. Hou, L. Sheng, W. Miller and L. Zhang, Approximating the spanning star forest problem and its applications to genomic sequence alignment, SIAM J. Comput. 38(3) (2008) 946–962], the authors introduced the MWSFP and proved its NP-hardness. They also gave a polynomial time algorithm for the MWSF problem when G is a tree. In this paper, we present a linear time algorithm that solves the MSWF problem when G is a cactus.

scholarly journals ON COMPUTING LONGEST PATHS IN SMALL GRAPH CLASSES

2007 ◽  
Vol 18 (05) ◽  
pp. 911-930 ◽  
Author(s):  
RYUHEI UEHARA ◽  
YUSHI UNO
Keyword(s):  
Linear Time ◽  
Hamiltonian Path ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Graph Classes ◽  
Longest Path ◽  
Longest Path Problem ◽  
Longest Paths ◽  
Interval Representations ◽  
The One

The longest path problem is the one that finds a longest path in a given graph. While the graph classes in which the Hamiltonian path problem can be solved efficiently are widely investigated, few graph classes are known to be solved efficiently for the longest path problem. Among those, for trees, a simple linear time algorithm for the longest path problem is known. We first generalize the algorithm, and show that the longest path problem can be solved efficiently for some tree-like graph classes by this approach. We next propose two new graph classes that have natural interval representations, and show that the longest path problem can be solved efficiently on these classes.

scholarly journals Linear Time Recognition of P4-Indifferent Graphs

1999 ◽  
Vol 6 (38) ◽  
Author(s):  
Romeo Rizzi
Keyword(s):  
Key Words ◽  
Linear Time ◽  
Time Algorithm ◽  
Simple Graph ◽  
Linear Time Algorithm ◽  
Induced Subgraphs ◽  
Modular Decomposition ◽  
Forbidden Induced Subgraphs ◽  
Chordless Path

<p>A simple graph is P4-indifferent if it admits a total order < on<br />its nodes such that every chordless path with nodes a, b, c, d and edges<br />ab, bc, cd has a < b < c < d or a > b > c > d. P4-indifferent graphs generalize<br /> indifferent graphs and are perfectly orderable. Recently, Hoang,<br />Maray and Noy gave a characterization of P4-indifferent graphs in<br />terms of forbidden induced subgraphs. We clarify their proof and describe<br /> a linear time algorithm to recognize P4-indifferent graphs. When<br />the input is a P4-indifferent graph, then the algorithm computes an order < as above.</p><p>Key words: P4-indifference, linear time, recognition, modular decomposition.</p><p> </p>

scholarly journals Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 293
Author(s):  
Xinyue Liu ◽  
Huiqin Jiang ◽  
Pu Wu ◽  
Zehui Shao
Keyword(s):  
Linear Time ◽  
Minimum Weight ◽  
Domination Number ◽  
Time Algorithm ◽  
Simple Graph ◽  
Linear Time Algorithm ◽  
Domination Problem ◽  
Np Complete ◽  
Chordal Bipartite Graphs ◽  
Dominating Function

For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v)≠0 has a neighbor u with f(u)≠0 for every vertex v∈V(G). The weight of a TR3DF f is the sum f(V)=∑v∈V(G)f(v) and the minimum weight of a total Roman {3}-dominating function on G is called the total Roman {3}-domination number denoted by γt{R3}(G). In this paper, we show that the total Roman {3}-domination problem is NP-complete for planar graphs and chordal bipartite graphs. Finally, we present a linear-time algorithm to compute the value of γt{R3} for trees.

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