Results 21 to 30 of about 119,166 (199)
Equitable colorings of outerplanar graphs
Discrete Mathematics, 2002 Abstract A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most 1. In this note, we prove the conjecture of Yap and Zhang that every outerplanar graph with maximum degree at most Δ admits an equitable k -coloring for every k ⩾1+ Δ /2. This restriction on k cannot be weakened.
Alexandr Kostochka
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On infinite outerplanar graphs [PDF]
Mathematica Bohemica, 1994 In this Note, we study infinite graphs with locally finite outerplane embeddings, given a characterization by forbidden ...
Boza Prieto, Luis +2 more
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Circular Separation Dimension of a Subclass of Planar Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 A pair of non-adjacent edges is said to be separated in a circular ordering of vertices, if the endpoints of the two edges do not alternate in the ordering.
Arpitha P. Bharathi +2 more
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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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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
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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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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 ...
Gronemann, Martin +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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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
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Large Induced Acyclic and Outerplanar Subgraphs of 2-Outerplanar Graph [PDF]
Graphs and Combinatorics, 2017 13 pages, 7 figures.
Glencora Borradaile +2 more
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