Results 21 to 30 of about 1,906 (145)
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.
Gregorio Hernández Peñalver +1 more
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Linear Algorithms for Isomorphism of Maximal Outerplanar Graphs [PDF]
Journal of the ACM, 1979 S. Mitchell, Terry Beyer, Whitney Jones
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Maximally Expressive GNNs for Outerplanar Graphs
Journal of Machine Learning Research, 2023 Most pharmaceutical molecules can be represented as outerplanar graphs. We propose a graph transformation that makes the Weisfeiler-Leman (WL) test and message passing graph neural networks maximally expressive on outerplanar graphs. While existing research predominantly focuses on enhancing expressivity of graph neural networks beyond the WL test on ...
Bause, Franka +3 more
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On the Vertex Separation of Maximal Outerplanar Graphs [PDF]
Serdica Journal of Computing, 2008 We investigate the NP-complete problem Vertex Separation (VS) on Maximal Outerplanar Graphs (mops). We formulate and prove a “main theorem for mops”, a necessary and sufficient condition for the vertex separation of a mop being k. The main theorem reduces the vertex separation of mops to a special kind of stretchability, one that we call affixability ...
Minko Markov
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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 +10 more sources
Dominating sets inducing large components in maximal outerplanar graphs [PDF]
Journal of Graph Theory, 2017 AbstractFor a maximal outerplanar graph G of order n at least three, Matheson and Tarjan showed that G has domination number at most . Similarly, for a maximal outerplanar graph G of order n at least five, Dorfling, Hattingh, and Jonck showed, by a completely different approach, that G has total domination number at most unless G is isomorphic to one ...
José D. Alvarado +2 more
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Irreducible nonmetrizable path systems in graphs
Journal of Graph Theory, Volume 102, Issue 1, Page 5-14, January 2023., 2023 Abstract A path system P ${\mathscr{P}}$ in a graph G =(V , E ) $G=(V,E)$ is a collection of paths with a unique u v $uv$ path for every two vertices u , v ∈ V $u,v\in V$. We say that P ${\mathscr{P}}$ is consistent if for any path P ∈ P $P\in {\mathscr{P}}$, every subpath of P $P$ is also in P ${\mathscr{P}}$.
Daniel Cizma, Nati Linial
wiley +1 more source
Longest and shortest cycles in random planar graphs
Random Structures &Algorithms, Volume 60, Issue 3, Page 462-505, May 2022., 2022 Abstract Let be a graph chosen uniformly at random from the class of all planar graphs on vertex set with edges. We study the cycle and block structure of when . More precisely, we determine the asymptotic order of the length of the longest and shortest cycle in in the critical range when .
Mihyun Kang, Michael Missethan
wiley +1 more source
Site percolation and isoperimetric inequalities for plane graphs
Random Structures &Algorithms, Volume 58, Issue 1, Page 150-163, January 2021., 2021 We use isoperimetric inequalities combined with a new technique to prove upper bounds for the site percolation threshold of plane graphs with given minimum degree conditions. In the process we prove tight new isoperimetric bounds for certain classes of hyperbolic graphs.
John Haslegrave, Christoforos Panagiotis
wiley +1 more source
Algorithm on rainbow connection for maximal outerplanar graphs [PDF]
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.
Xingchao Deng, Hengzhe Li, Guiying Yan
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