Results 11 to 20 of about 1,769 (162)
Counting outerplanar maps [PDF]
The Electronic Journal of Combinatorics, 2017 A map is outerplanar if all its vertices lie in the outer face. We enumerate various classes of rooted outerplanar maps with respect to the number of edges and vertices. The proofs involve several bijections with lattice paths.
Geffner, I., Noy Serrano, Marcos
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Pathwidth of outerplanar graphs [PDF]
Journal of Graph Theory, 2006 We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin, after having proved that the pathwidth of every biconnected outerplanar graph is always at most ...
Coudert, David +2 more
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Characterizations of outerplanar graphs [PDF]
Discrete Mathematics, 1979 The paper presents several characterizations of outerplanar graphs, some of them are counterparts of the well-known characterizations of planar graphs and the other provide very efficient tools for outerplanarity testing, coding (i.e. isomorphism testing)
Sysło, Maciej M., Maciej M. Sysło
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Outerplanar Partitions of Planar Graphs [PDF]
Journal of Combinatorial Theory, Series B, 1996 Anouterplanargraph is one that can be embedded in the plane so that all of the vertices lie on one of the faces. We investigate a conjecture of Chartrand, Geller, and Hedetniemi, that every planar graph can be edge-partitioned into two outerplanar ...
Kedlaya, Kiran S.
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Outerplanar partial cubes [PDF]
, 2022 Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Kolja Knauer[en] The class of outerplanar graphs is minor-closed and can be characterized by two excluded minors: ${\mathbf{}}K_{4}$ and $K_{
Rovira Segú, Bernat
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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
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Large Induced Acyclic and Outerplanar Subgraphs of 2-Outerplanar Graph [PDF]
Graphs and Combinatorics, 2017 Albertson and Berman conjectured that every planar graph has an induced forest on half of its vertices. The best known lower bound, due to Borodin, is that every planar graph has an induced forest on two fifths of its vertices. In a related result, Chartran and Kronk, proved that the vertices of every planar graph can be partitioned into three sets ...
Glencora Borradaile +2 more
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Outerplanar and Planar Oriented Cliques [PDF]
Journal of Graph Theory, 2015 AbstractThe clique number of an undirected graph G is the maximum order of a complete subgraph of G and is a well‐known lower bound for the chromatic number of G. Every proper k‐coloring of G may be viewed as a homomorphism (an edge‐preserving vertex mapping) of G to the complete graph of order k.
Ayan Nandy +2 more
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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 +2 more
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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