Results 51 to 60 of about 168 (119)
A Note on the Fair Domination Number in Outerplanar Graphs
Discussiones Mathematicae Graph Theory, 2020 For k ≥ 1, a k-fair dominating set (or just kFD-set), in a graph G is a dominating set S such that |N(v) ∩ S| = k for every vertex v ∈ V − S. The k-fair domination number of G, denoted by fdk(G), is the minimum cardinality of a kFD-set. A fair dominating
Hajian Majid, Rad Nader Jafari
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Improved Bounds for Track Numbers of Planar Graphs
Journal of Graph Algorithms and Applications, 2020 A track layout of a graph consists of a vertex coloring and a total order of each color class, such that no two edges cross between any two color classes.
Sergey Pupyrev
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Scaling Limits of Random Graphs from Subcritical Classes: Extended abstract [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We study the uniform random graph $\mathsf{C}_n$ with $n$ vertices drawn from a subcritical class of connected graphs. Our main result is that the rescaled graph $\mathsf{C}_n / \sqrt{n}$ converges to the Brownian Continuum Random Tree $\mathcal{T}_ ...
Konstantinos Panagiotou +2 more
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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
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Indonesian Journal of CombinatoricsA planar graph is said to be zonal when is possible to label its vertices with the nonzero elements of ℤ3, in such a way that the sum of the labels of the vertices on the boundary of each zone is 0 in ℤ3.
Christian Barrientos, Sarah Minion
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An O(mn2) Algorithm for Computing the Strong Geodetic Number in Outerplanar Graphs
Discussiones Mathematicae Graph Theory, 2022 Let G = (V (G), E(G)) be a graph and S be a subset of vertices of G. Let us denote by γ[u, v] a geodesic between u and v. Let Γ(S) = {γ[vi, vj] | vi, vj ∈ S} be a set of exactly |S|(|S|−1)/2 geodesics, one for each pair of distinct vertices in S.
Mezzini Mauro
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Approximation Algorithms for the Maximum Induced Planar and Outerplanar Subgraph Problems
Journal of Graph Algorithms and Applications, 2007 The task of finding the largest subset of vertices of a graph that induces a planar subgraph is known as the Maximum Induced Planar Subgraph problem (MIPS). In this paper, some new approximation algorithms for MIPS are introduced.
Kerri Morgan, Graham Farr
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On the Relationships between Zero Forcing Numbers and Certain Graph Coverings
Special Matrices, 2014 The zero forcing number and the positive zero forcing number of a graph are two graph parameters that arise from two types of graph colourings. The zero forcing number is an upper bound on the minimum number of induced paths in the graph that cover all ...
Taklimi Fatemeh Alinaghipour +2 more
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Planar embeddability of the vertices of a graph using a fixed point set is NP-hard
Journal of Graph Algorithms and Applications, 2006 Let G=(V,E) be a graph with n vertices and let P be a set of n points in the plane. We show that deciding whether there is a planar straight-line embedding of G such that the vertices V are embedded onto the points P is NP-complete, even when G is 2 ...
Sergio Cabello
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Vertex Colorings without Rainbow Subgraphs
Discussiones Mathematicae Graph Theory, 2016 Given a coloring of the vertices of a graph G, we say a subgraph is rainbow if its vertices receive distinct colors. For a graph F, we define the F-upper chromatic number of G as the maximum number of colors that can be used to color the vertices of G ...
Goddard Wayne, Xu Honghai
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