Results 31 to 40 of about 147,831 (333)
Enumeration of labelled 4-regular planar graphs [PDF]
, 2019 We present the first combinatorial scheme for counting labelled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function of labelled 4-regular planar graphs can be computed ...
Noy, Marc +2 more
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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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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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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 degree/diameter problem in maximal planar bipartite graphs [PDF]
, 2014 The (¿;D) (degree/diameter) problem consists of nding the largest possible number of vertices n among all the graphs with maximum degree ¿ and diameter D.
Dalfó Simó, Cristina +2 more
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Weak Degeneracy of Planar Graphs and Locally Planar Graphs
The Electronic Journal of Combinatorics, 2023 Weak degeneracy is a variation of degeneracy which shares many nice properties of degeneracy. In particular, if a graph $G$ is weakly $d$-degenerate, then for any $(d+1)$-list assignment $L$ of $G$, one can construct an $L$ coloring of $G$ by a modified greedy coloring algorithm.
Han, Ming +4 more
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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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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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Planar graphs without {4,6,8}-cycles are 3-choosable
AIMS Mathematics, 2021 In 2018, Dvořák and Postle introduced DP-coloring and proved that planar graphs without cycles of lengths 4 to 8 are 3-choosable. In this paper, we prove that planar graphs without {4,6,8}-cycles are 3-choosable by using the technique developed in DP ...
Yueying Zhao, Lianying Miao
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