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Pathwidth of outerplanar graphs [PDF]

Journal of Graph Theory, 2006
AbstractWe are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin [3], after having proved that the pathwidth of every biconnected outerplanar graph is always at most twice the pathwidth of its (geometric) dual plus two, conjectured that there exists a ...
Coudert, David, Huc, Florian, Sereni, Jean-Sébastien   +2 more
core   +11 more sources

Image contraction through fuzzy soft outerplanar graph structures. [PDF]

Sci Rep
Fuzzy sets and soft sets serve as powerful mathematical tools to handle uncertainty and vagueness in real-world problems. Building on these, this study introduces the concept of fuzzy soft outerplanar graphs (FSOGs), a fusion of fuzzy soft set theory ...
Jaisankar D, Ramalingam S, Zegeye GB.
europepmc   +2 more sources

Bipolar fuzzy outerplanar graphs approach in image shrinking. [PDF]

Sci Rep
Bipolar fuzzy outerplanar graphs are interesting and significant subclasses within the broader field of fuzzy graph theory. In this paper, bipolar fuzzy outerplanar graphs, and its properties are introduced.
Jaisankar D, Ramalingam S, Deivanayagampillai N, Walelign T.   +3 more
europepmc   +2 more sources

A fuzzy graph theoretic approach to face shape recognition using cubic outerplanar structures. [PDF]

Sci Rep
The well-known topic of crisp graph planarity is contrasted with the more new and thoroughly studied field of planarity inside a fuzzy framework. In cubic fuzzy domain, cubic multisets with interval and fuzzy number to capture vagueness.
Jaisankar D, Ramalingam S, Zegeye GB.
europepmc   +2 more sources

Pathlength of Outerplanar Graphs

Theoretical Computer Science, 2022
A path-decomposition of a graph G = (V, E) is a sequence of subsets of V , called bags, that satisfy some connectivity properties. The length of a path-decomposition of a graph G is the greatest distance between two vertices that belong to a same bag and the pathlength, denoted by pl(G), of G is the smallest length of its path-decompositions.
Dissaux, Thomas, Nisse, Nicolas
openaire   +6 more sources

Edge-group choosability of outerplanar and near-outerplanar graphs [PDF]

Transactions on Combinatorics, 2020
Let $\chi_{gl}(G)$ be the {\it{group choice number}} of $G$. A graph $G$ is called {\it{edge-$k$-group choosable}} if its line graph is $k$-group choosable. The {\it{group-choice index}} of $G$, $\chi'_{gl}(G)$, is the smallest $k$ such that $G$ is edge-$
Amir Khamseh
doaj   +1 more source

Monotonic Representations of Outerplanar Graphs as Edge Intersection Graphs of Paths on a Grid

Journal of Graph Algorithms and Applications, 2022
In a representation of a graph $G$ as an edge intersection graph of paths on a grid (EPG) every vertex of $G$ is represented by a path on a grid and two paths share a grid edge iff the corresponding vertices are adjacent.
Eranda Çela, Elisabeth Gaar
doaj   +1 more source

Splitting Plane Graphs to Outerplanarity

Journal of Graph Algorithms and Applications, 2023
Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph editing operation to achieve desired properties with as few splits as possible, most often planarity, for which the problem is NP-hard.Here we study how to minimize the number of splits to turn a plane graph ...
Martin Gronemann, Martin Nöllenburg, Anaïs Villedieu   +2 more
openaire   +3 more sources

Circular Separation Dimension of a Subclass of Planar Graphs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2017
A pair of non-adjacent edges is said to be separated in a circular ordering of vertices, if the endpoints of the two edges do not alternate in the ordering.
Arpitha P. Bharathi, Minati De, Abhiruk Lahiri   +2 more
doaj   +1 more source

On the planarity of line Mycielskian graph of a graph

Ratio Mathematica, 2020
The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤  i ≤  q and e, then for 1 ≤  i ≤  q , joining ei' to the neighbours of ei  and  to e.
Keerthi G. Mirajkar, Anuradha V Deshpande   +1 more
doaj   +1 more source