Results 41 to 50 of about 119 (107)
Random graphs embeddable in order‐dependent surfaces
Random Structures &Algorithms, Volume 64, Issue 4, Page 940-985, July 2024.Abstract Given a ‘genus function’ g=g(n)$$ g=g(n) $$, we let Eg$$ {\mathcal{E}}^g $$ be the class of all graphs G$$ G $$ such that if G$$ G $$ has order n$$ n $$ (i.e., has n$$ n $$ vertices) then it is embeddable in a surface of Euler genus at most g(n)$$ g(n) $$.
Colin McDiarmid, Sophia Saller
wiley +1 more source
On tree decompositions whose trees are minors
Journal of Graph Theory, Volume 106, Issue 2, Page 296-306, June 2024.Abstract In 2019, Dvořák asked whether every connected graph G $G$ has a tree decomposition ( T , B ) $(T,{\rm{ {\mathcal B} }})$ so that T $T$ is a subgraph of G $G$ and the width of ( T , B ) $(T,{\rm{ {\mathcal B} }})$ is bounded by a function of the treewidth of G $G$.
Pablo Blanco +5 more
wiley +1 more source
The product structure of squaregraphs
Journal of Graph Theory, Volume 105, Issue 2, Page 179-191, February 2024.Abstract A squaregraph is a plane graph in which each internal face is a 4‐cycle and each internal vertex has degree at least 4. This paper proves that every squaregraph is isomorphic to a subgraph of the semistrong product of an outerplanar graph and a path.
Robert Hickingbotham +3 more
wiley +1 more source
Secure total domination number in maximal outerplanar graphs
Discrete Applied MathematicsA subset $S$ of vertices in a graph $G$ is a secure total dominating set of $G$ if $S$ is a total dominating set of $G$ and, for each vertex $u \not\in S$, there is a vertex $v \in S$ such that $uv$ is an edge and $(S \setminus \{v\}) \cup \{u\}$ is also a total dominating set of $G$.
Yasufumi Aita, Toru Araki
openaire +3 more sources
Eternal vertex cover number of maximal outerplanar graphs
, 2022 Eternal vertex cover problem is a variant of the classical vertex cover problem modeled as a two player attacker-defender game. Computing eternal vertex cover number of graphs is known to be NP-hard in general and the complexity status of the problem for bipartite graphs is open.
Babu, Jasine +3 more
openaire +2 more sources
On dominating sets of maximal outerplanar graphs
Discrete Applied Mathematics, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Campos, C.N., Wakabayashi, Y.
openaire +1 more source
Location in maximal outerplanar graphs
, 2017 In this work we study the metric dimension and the location-domination number of maximal outerplanar graphs. Concretely, we determine tight upper and lower bounds on the metric dimension and characterize those maximal outerplanar graphs attaining the lower bound. We also give a lower bound on the location-domination number
Claverol Aguas, Mercè +6 more
openaire +1 more source
Dominating sets of maximal outerplanar graphs
Discrete Applied Mathematics, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
Maximal outerplanar graphs as chordal graphs, path-neighborhood graphs, and triangle graphs [PDF]
Australasian Journal of Combinatorics, 2011 Maximal outerplanar graphs are characterized using three different classes of graphs. A path-neighborhood graph is a connected graph in which every neighborhood induces a path. The triangle graph $T(G)$ has the triangles of the graph $G$ as its vertices, two of these being adjacent whenever as triangles in $G$ they share an edge.
Laskar, RC, Mulder, Martyn, Novick, B
openaire +3 more sources
Algorithm on rainbow connection for maximal outerplanar graphs
Theoretical Computer Science, 2016 In this paper, we consider rainbow connection number of maximal outerplanar graphs(MOPs) on algorithmic aspect. For the (MOP) $G$, we give sufficient conditions to guarantee that $rc(G) = diam(G).$ Moreover, we produce the graph with given diameter $d$ and give their rainbow coloring in linear time. X.Deng et al.
Deng, Xingchao +2 more
openaire +2 more sources