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Algorithms for Outerplanar Graph Roots and Graph Roots of Pathwidth at Most 2 [PDF]
Algorithmica, 2017 Deciding if a graph has a square root is a classical problem, which has been studied extensively both from graph-theoretic and algorithmic perspective. As the problem is NP-complete, substantial effort has been dedicated to determining the complexity of ...
P. Golovach +4 more
semanticscholar +1 more source
Free Choosability of Outerplanar Graphs [PDF]
Graphs and Combinatorics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aubry, Yves +2 more
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Irreducible nonmetrizable path systems in graphs
Journal of Graph Theory, Volume 102, Issue 1, Page 5-14, January 2023., 2023 Abstract A path system P ${\mathscr{P}}$ in a graph G =(V , E ) $G=(V,E)$ is a collection of paths with a unique u v $uv$ path for every two vertices u , v ∈ V $u,v\in V$. We say that P ${\mathscr{P}}$ is consistent if for any path P ∈ P $P\in {\mathscr{P}}$, every subpath of P $P$ is also in P ${\mathscr{P}}$.
Daniel Cizma, Nati Linial
wiley +1 more source
Pathwidth of outerplanar graphs [PDF]
Journal of Graph Theory, 2006 We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin, after having proved that the pathwidth of every biconnected outerplanar graph is always at most twice the pathwidth of its (geometric) dual plus two, conjectured that there exists a constant $c ...
Coudert, David +2 more
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Longest and shortest cycles in random planar graphs
Random Structures &Algorithms, Volume 60, Issue 3, Page 462-505, May 2022., 2022 Abstract Let be a graph chosen uniformly at random from the class of all planar graphs on vertex set with edges. We study the cycle and block structure of when . More precisely, we determine the asymptotic order of the length of the longest and shortest cycle in in the critical range when .
Mihyun Kang, Michael Missethan
wiley +1 more source
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
doaj +1 more source
Site percolation and isoperimetric inequalities for plane graphs
Random Structures &Algorithms, Volume 58, Issue 1, Page 150-163, January 2021., 2021 We use isoperimetric inequalities combined with a new technique to prove upper bounds for the site percolation threshold of plane graphs with given minimum degree conditions. In the process we prove tight new isoperimetric bounds for certain classes of hyperbolic graphs.
John Haslegrave, Christoforos Panagiotis
wiley +1 more source
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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On k-edge-magic labelings of maximal outerplanar graphs
AKCE International Journal of Graphs and Combinatorics, 2015 Let G be a graph with vertex set V and edge set E such that |V|=p and |E|=q. We denote this graph by (p,q)-graph. For integers k≥0, define a one-to-one map f from E to {k,k+1,…,k+q−1} and define the vertex sum for a vertex v as the sum of the labels of ...
Gee-Choon Lau +3 more
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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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