Results 31 to 40 of about 17,262 (262)
Planar Transitive Graphs [PDF]
The Electronic Journal of Combinatorics, 2018 We prove that the first homology group of every planar locally finite transitive graph $G$ is finitely generated as an $\Aut(G)$-module and we prove a similar result for the fundamental group of locally finite planar Cayley graphs. Corollaries of these results include Droms's theorem that planar groups are finitely presented and Dunwoody's theorem that
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NP-Completeness Results for Minimum Planar Spanners [PDF]
Discrete Mathematics & Theoretical Computer Science, 1998 For any fixed parameter t greater or equal to 1, a t-spanner of a graph G is a spanning subgraph in which the distance between every pair of vertices is at most t times their distance in G.
Ulrik Brandes, Dagmar Handke
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Negative results on acyclic improper colorings [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Raspaud and Sopena showed that the oriented chromatic number of a graph with acyclic chromatic number $k$ is at most $k2^{k-1}$. We prove that this bound is tight for $k \geq 3$.
Pascal Ochem
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The structure and the list 3-dynamic coloring of outer-1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 An outer-1-planar graph is a graph admitting a drawing in the plane so that all vertices appear in the outer region of the drawing and every edge crosses at most one other edge.
Yan Li, Xin Zhang
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A Linear Kernel for Planar Total Dominating Set [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 A total dominating set of a graph $G=(V,E)$ is a subset $D \subseteq V$ such that every vertex in $V$ is adjacent to some vertex in $D$. Finding a total dominating set of minimum size is NP-hard on planar graphs and W[2]-complete on general graphs when ...
Valentin Garnero, Ignasi Sau
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L(2, 1)-Labelings of Some Families of Oriented Planar Graphs
Discussiones Mathematicae Graph Theory, 2014 In this paper we determine, or give lower and upper bounds on, the 2-dipath and oriented L(2, 1)-span of the family of planar graphs, planar graphs with girth 5, 11, 16, partial k-trees, outerplanar graphs and cacti.
Sen Sagnik
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Planar Graphs under Pythagorean Fuzzy Environment
Mathematics, 2018 Graph theory plays a substantial role in structuring and designing many problems. A number of structural designs with crossings can be found in real world scenarios. To model the vagueness and uncertainty in graphical network problems, many extensions of
Muhammad Akram +2 more
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On almost hypohamiltonian graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 A graph $G$ is almost hypohamiltonian (a.h.) if $G$ is non-hamiltonian, there exists a vertex $w$ in $G$ such that $G - w$ is non-hamiltonian, and $G - v$ is hamiltonian for every vertex $v \ne w$ in $G$. The second author asked in [J.
Jan Goedgebeur, Carol T. Zamfirescu
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A Note on Edge-Group Choosability of Planar Graphs without 5-Cycles
Journal of Mathematics, 2020 This paper is devoted to a study of the concept of edge-group choosability of graphs. We say that G is edge-k-group choosable if its line graph is k-group choosable.
Amir Khamseh
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Algorithmic Aspects of Some Variations of Clique Transversal and Clique Independent Sets on Graphs
Algorithms, 2021 This paper studies the maximum-clique independence problem and some variations of the clique transversal problem such as the {k}-clique, maximum-clique, minus clique, signed clique, and k-fold clique transversal problems from algorithmic aspects for k ...
Chuan-Min Lee
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