Results 31 to 40 of about 119,166 (199)
Approximation of pathwidth of outerplanar graphs [PDF]
Journal of Algorithms, 2001 There exists a polynomial time algorithm to compute the pathwidth of outerplanar graphs, but the large exponent makes this algorithm impractical. In this paper, we give an algorithm that, given a biconnected outerplanar graph G, finds a path decomposition of G of pathwidth at most twice the pathwidth of G plus one.
Hans L. Bodlaender, Fedor V. Fomin
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Strong Chromatic Index of Outerplanar Graphs
Axioms, 2022 The strong chromatic index χs′(G) of a graph G is the minimum number of colors needed in a proper edge-coloring so that every color class induces a matching in G. It was proved In 2013, that every outerplanar graph G with Δ≥3 has χs′(G)≤3Δ−3.
Ying Wang +3 more
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Transactions on Combinatorics, 2022 An optimal labeling of a graph with $n$ vertices and $m$ edges is an injective assignment of the first $n$ nonnegative integers to the vertices, that induces, for each edge, a weight given by the sum of the labels of its end-vertices with the ...
Christian Barrientos, Maged Youssef
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Monitoring maximal outerplanar graphs [PDF]
Electronic Notes in Discrete Mathematics, 2014 In this paper we define a new concept of monitoring the elements of triangulation graphs by faces. Furthermore, we analyze this, and other monitoring concepts (by vertices and by edges), from a combinatorial point of view, on maximal outerplanar graphs.
Martins, Mafalda, Hernández, Gregorio
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Alpha Labeling of Amalgamated Cycles
Theory and Applications of Graphs, 2022 A graceful labeling of a bipartite graph is an \a-labeling if it has the property that the labels assigned to the vertices of one stable set of the graph are smaller than the labels assigned to the vertices of the other stable set.
Christian Barrientos
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Nullspace Embeddings for Outerplanar Graphs [PDF]
, 2017 21 pages.
Alexander Schrijver, László Lovász
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On the Edge-Length Ratio of Outerplanar Graphs [PDF]
Theoretical Computer Science, 2018 We show that any outerplanar graph admits a planar straightline drawing such that the length ratio of the longest to the shortest edges is strictly less than 2. This result is tight in the sense that for any $ > 0$ there are outerplanar graphs that cannot be drawn with an edge-length ratio smaller than $2 - $.
Lazard S., Lenhart W. J., Liotta G.
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Star edge coloring of $ K_{2, t} $-free planar graphs
AIMS Mathematics, 2023 The star chromatic index of a graph $ G $, denoted by $ \chi{'}_{st}(G) $, is the smallest number of colors required to properly color $ E(G) $ such that every connected bicolored subgraph is a path with no more than three edges.
Yunfeng Tang , Huixin Yin , Miaomiao Han
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A Note on Edge‐Group Choosability of Planar Graphs without 5‐Cycles
Journal of Mathematics, Volume 2020, Issue 1, 2020., 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. In this paper, we study an edge‐group choosability version of Vizing conjecture for planar graphs without 5‐cycles and for planar graphs without noninduced 5‐cycles (2010 Mathematics ...
Amir Khamseh, Andrei V. Kelarev
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A generalization of outerplanar graphs
Discrete Mathematics, 1984 AbstractLet G be a planar graph and W a set of vertices, G is W-outerplanar if it can be embedded in the plane so that all vertices of W lie on the exterior face. We give a characterization of these graphs by forbidden subgraphs, an upper bound on the number of edges, and other properties which lead to an algorithm of W-outerplanarity testing.
Lía Oubiña, R. Zucchello
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