Results 11 to 20 of about 161 (144)
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 +1 more
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Pathlength of Outerplanar Graphs
, 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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Free Choosability of Outerplanar Graphs [PDF]
Graphs and Combinatorics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aubry, Yves +2 more
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Outerplanar Graph Drawings with Few Slopes [PDF]
Computational Geometry, 2012 We consider straight-line outerplanar drawings of outerplanar graphs in which a small number of distinct edge slopes are used, that is, the segments representing edges are parallel to a small number of directions. We prove that $ -1$ edge slopes suffice for every outerplanar graph with maximum degree $ \ge 4$.
Knauer, Kolja +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
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 twice the pathwidth of its (geometric) dual plus two, conjectured that there exists a constant $c ...
Coudert, David +2 more
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Double domination in maximal outerplanar graphs
Open Mathematics, 2022 In graph GG, a vertex dominates itself and its neighbors. A subset S⊆V(G)S\subseteq V\left(G) is said to be a double-dominating set of GG if SS dominates every vertex of GG at least twice.
Zhuang Wei, Zheng Qiuju
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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
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On the spread of outerplanar graphs
Special Matrices, 2022 The spread of a graph is the difference between the largest and most negative eigenvalue of its adjacency matrix. We show that for sufficiently large nn, the nn-vertex outerplanar graph with maximum spread is a vertex joined to a linear forest with Ω(n ...
Gotshall Daniel +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