Results 61 to 70 of about 231 (167)
On vertex‐transitive graphs with a unique hamiltonian cycle
Journal of Graph Theory, Volume 108, Issue 1, Page 65-99, January 2025.Abstract A graph is said to be uniquely hamiltonian if it has a unique hamiltonian cycle. For a natural extension of this concept to infinite graphs, we find all uniquely hamiltonian vertex‐transitive graphs with finitely many ends, and also discuss some examples with infinitely many ends.
Babak Miraftab, Dave Witte Morris
wiley +1 more source
Characterizations of outerplanar graphs
Discrete Mathematics, 1979 AbstractThe paper presents several characterizations of outerplanar graphs, some of them are counterparts of the well-known characterizations of planar graphs and the other provide very efficient tools for outerplanarity testing, coding (i.e. isomorphism testing), and counting such graphs.
openaire +1 more source
Computing Minimum Cycle Bases in Weighted Partial 2-Trees in Linear Time
Journal of Graph Algorithms and Applications, 2014 We present a linear time algorithm for computing an implicit linear space representation of a minimum cycle basis in weighted partial 2-trees (i.e., graphs of treewidth at most two) with non-negative edge-weights. The implicit representation can be made
Carola Doerr +2 more
doaj +1 more source
On the Hub Number of Ring Graphs and Their Behavior Under Graph Operations
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.This study examines the hub number of ring graphs and investigates their behavior under operations such as union, intersection, and join. Different findings for this parameter are found for a variety of types of ring graphs, such as commutative ring graphs, path ring graphs, complete ring graphs, cycle ring graphs, and star ring graphs, for which the ...
Mohammed Alsharafi +3 more
wiley +1 more source
Self‐avoiding walks and polygons on hyperbolic graphs
Journal of Graph Theory, Volume 106, Issue 3, Page 435-473, July 2024.Abstract We prove that for the d $d$‐regular tessellations of the hyperbolic plane by k $k$‐gons, there are exponentially more self‐avoiding walks of length n $n$ than there are self‐avoiding polygons of length n $n$. We then prove that this property implies that the self‐avoiding walk is ballistic, even on an arbitrary vertex‐transitive graph ...
Christoforos Panagiotis
wiley +1 more source
Random graphs embeddable in order‐dependent surfaces
Random Structures &Algorithms, Volume 64, Issue 4, Page 940-985, July 2024.Abstract Given a ‘genus function’ g=g(n)$$ g=g(n) $$, we let Eg$$ {\mathcal{E}}^g $$ be the class of all graphs G$$ G $$ such that if G$$ G $$ has order n$$ n $$ (i.e., has n$$ n $$ vertices) then it is embeddable in a surface of Euler genus at most g(n)$$ g(n) $$.
Colin McDiarmid, Sophia Saller
wiley +1 more source
Outerplanar and Forest Storyplans
An earlier version of this paper has appeared in Proc.
Jiří Fiala +4 more
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On the colorings of outerplanar graphs
Discrete Mathematics, 1995 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Straight-Line Drawings on Restricted Integer Grids in Two and Three Dimensions
Journal of Graph Algorithms and Applications, 2003 This paper investigates the following question: Given a grid ϕ, where ϕ is a proper subset of the integer 2D or 3D grid, which graphs admit straight-line crossing-free drawings with vertices located at (integral) grid points of ϕ?
Stefan Felsner +2 more
doaj +1 more source
On tree decompositions whose trees are minors
Journal of Graph Theory, Volume 106, Issue 2, Page 296-306, June 2024.Abstract In 2019, Dvořák asked whether every connected graph G $G$ has a tree decomposition ( T , B ) $(T,{\rm{ {\mathcal B} }})$ so that T $T$ is a subgraph of G $G$ and the width of ( T , B ) $(T,{\rm{ {\mathcal B} }})$ is bounded by a function of the treewidth of G $G$.
Pablo Blanco +5 more
wiley +1 more source