Results 31 to 40 of about 4,003 (201)
A generalization of outerplanar graphs
Discrete Mathematics, 1984 A graph G is said to be W-outerplanar if it can be embedded in the plane so that all vertices of a given set \(W\subset V(G)\) lie on the boundary of one face. A characterization of such graphs is given by means of forbidden subgraphs, and an algorithm for W-outerplanarity testing is described. The results overlap, in part, with those of \textit{V.
Lía Oubiña, R. Zucchello
openaire +3 more sources
Alpha Labeling of Amalgamated Cycles
Theory and Applications of Graphs, 2022 A graceful labeling of a bipartite graph is an \a-labeling if it has the property that the labels assigned to the vertices of one stable set of the graph are smaller than the labels assigned to the vertices of the other stable set.
Christian Barrientos
doaj +1 more source
Space-Efficient Biconnected Components and Recognition of Outerplanar Graphs [PDF]
, 2016 We present space-efficient algorithms for computing cut vertices in a given graph with $n$ vertices and $m$ edges in linear time using $O(n+\min\{m,n\log \log n\})$ bits.
Kammer, Frank +2 more
core +2 more sources
Monitoring maximal outerplanar graphs [PDF]
Electronic Notes in Discrete Mathematics, 2014 In this paper we define a new concept of monitoring the elements of triangulation graphs by faces. Furthermore, we analyze this, and other monitoring concepts (by vertices and by edges), from a combinatorial point of view, on maximal outerplanar graphs.
Martins, Mafalda, Hernández, Gregorio
openaire +3 more sources
Definability Equals Recognizability for $k$-Outerplanar Graphs [PDF]
, 2015 One of the most famous algorithmic meta-theorems states that every graph property that can be defined by a sentence in counting monadic second order logic (CMSOL) can be checked in linear time for graphs of bounded treewidth, which is known as Courcelle ...
Bodlaender, Hans L., Jaffke, Lars
core +5 more sources
Star edge coloring of $ K_{2, t} $-free planar graphs
AIMS Mathematics, 2023 The star chromatic index of a graph $ G $, denoted by $ \chi{'}_{st}(G) $, is the smallest number of colors required to properly color $ E(G) $ such that every connected bicolored subgraph is a path with no more than three edges.
Yunfeng Tang , Huixin Yin , Miaomiao Han
doaj +1 more source
On the Edge-Length Ratio of Outerplanar Graphs [PDF]
Theoretical Computer Science, 2018 We show that any outerplanar graph admits a planar straightline drawing such that the length ratio of the longest to the shortest edges is strictly less than 2. This result is tight in the sense that for any $ > 0$ there are outerplanar graphs that cannot be drawn with an edge-length ratio smaller than $2 - $.
Lazard, Sylvain +2 more
openaire +5 more sources
On the Planarity of Generalized Line Graphs
Theory and Applications of Graphs, 2019 One of the most familiar derived graphs is the line graph. The line graph $L(G)$ of a graph $G$ is that graph whose vertices are the edges of $G$ where two vertices of $L(G)$ are adjacent if the corresponding edges are adjacent in~$G$.
Khawlah H. Alhulwah +2 more
doaj +1 more source
On an interpolation property of outerplanar graphs
Discrete Applied Mathematics, 2006 Let \(D\) be an acyclic orientation of a graph \(G\). An arc of \(D\) is dependent if a directed cycle is created when it is reversed. Denote by \(d(D)\) the number of dependent arcs in \(D\). Let \(d_{\min}(G)\) be the minimum \(d(D)\), and \(d_{\max}(G)\) the maximum \(d(D)\), over all acyclic orientations \(D\) of \(G\).
Li-Da Tong, Ko-Wei Lih, Chen-Ying Lin
openaire +2 more sources
The Degree-Diameter Problem for Outerplanar Graphs
Discussiones Mathematicae Graph Theory, 2017 For positive integers Δ and D we define nΔ,D to be the largest number of vertices in an outerplanar graph of given maximum degree Δ and diameter D. We prove that nΔ,D=ΔD2+O (ΔD2−1)$n_{\Delta ,D} = \Delta ^{{D \over 2}} + O\left( {\Delta ^{{D \over 2 ...
Dankelmann Peter +2 more
doaj +1 more source