Results 11 to 20 of about 119,166 (199)
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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Edge-group choosability of outerplanar and near-outerplanar graphs [PDF]
Transactions on Combinatorics, 2020 Let $\chi_{gl}(G)$ be the {\it{group choice number}} of $G$. A graph $G$ is called {\it{edge-$k$-group choosable}} if its line graph is $k$-group choosable. The {\it{group-choice index}} of $G$, $\chi'_{gl}(G)$, is the smallest $k$ such that $G$ is edge-$
Amir Khamseh
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Adjacency posets of outerplanar graphs [PDF]
Discrete Mathematics Volume 344, Issue 5, May 2021, 112338, 2020 Felsner, Li and Trotter showed that the dimension of the adjacency poset of an outerplanar graph is at most 5, and gave an example of an outerplanar graph whose adjacency poset has dimension 4. We improve their upper bound to 4, which is then best possible.
arxiv +5 more sources
Outerplanar graph drawings with few slopes [PDF]
Comput.Geom. 47 (2014) 614-624, 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 $\Delta-1$ edge slopes suffice for every outerplanar graph with maximum degree $\Delta\ge 4$.
Knauer, Kolja +2 more
arxiv +10 more sources
Metric dimension of maximal outerplanar graphs [PDF]
Bull. Malays. Math. Sci. Soc. (2021) 44:2603-2630, 2019 In this paper, we study the metric dimension problem in maximal outerplanar graphs. Concretely, if $\beta (G)$ is the metric dimension of a maximal outerplanar graph $G$ of order $n$, we prove that $2\le \beta (G) \le \lceil \frac{2n}{5}\rceil$ and that the bounds are tight. We also provide linear algorithms to decide whether the metric dimension of $G$
M. Claverol +6 more
arxiv +7 more sources
On the number of series parallel and outerplanar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We show that the number $g_n$ of labelled series-parallel graphs on $n$ vertices is asymptotically $g_n \sim g \cdot n^{-5/2} \gamma^n n!$, where $\gamma$ and $g$ are explicit computable constants.
Manuel Bodirsky +3 more
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The Planar Index and Outerplanar Index of Some Graphs Associated to Commutative Rings
Discussiones Mathematicae - General Algebra and Applications, 2019 In this paper, we study the planar and outerplanar indices of some graphs associated to a commutative ring. We give a full characterization of these graphs with respect to their planar and outerplanar indices when R is a finite ring.
Barati Zahra, Afkhami Mojgan
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COLORING THE SQUARE OF AN OUTERPLANAR GRAPH [PDF]
Taiwanese Journal of Mathematics, 2006 Let $G$ be an outerplanar graph with maximum degree $\Delta(G)\ge 3$. We prove that the chromatic number $\chi(G^2)$ of the square of $G$ is at most $\Delta(G)+2$. This confirms a conjecture of Wegner [8] for outerplanar graphs. The upper bound can be further reduced to the optimal value $\Delta(G)+1$ when $\Delta(G)\ge 7$.
Ko‐Wei Lih, Weifan Wang
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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.
Thomas Dissaux, Nicolas Nisse
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Free Choosability of Outerplanar Graphs [PDF]
Graphs and Combinatorics, 2015 A graph G is free (a, b)-choosable if for any vertex v with b colors assigned and for any list of colors of size a associated with each vertex $$u\ne v$$u?v, the coloring can be completed by choosing for u a subset of b colors such that adjacent vertices are colored with disjoint color sets.
Yves Aubry +2 more
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