Results 21 to 30 of about 875,640 (148)
Recognizing Trees From Incomplete Decks
Journal of Graph Theory, Volume 110, Issue 3, Page 322-336, November 2025.ABSTRACT Given a graph G, the unlabeled subgraphs G − v are called the cards of G. The deck of G is the multiset { G − v : v ∈ V ( G ) }. Wendy Myrvold showed that a disconnected graph and a connected graph both on n vertices have at most ⌊ n 2 ⌋ + 1 cards in common and found (infinite) families of trees and disconnected forests for which this upper ...
Gabriëlle Zwaneveld
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On Endomorphism Universality of Sparse Graph Classes
Journal of Graph Theory, Volume 110, Issue 2, Page 223-244, October 2025.ABSTRACT We show that every commutative idempotent monoid (a.k.a. lattice) is the endomorphism monoid of a subcubic graph. This solves a problem of Babai and Pultr and the degree bound is best‐possible. On the other hand, we show that no class excluding a minor can have all commutative idempotent monoids among its endomorphism monoids. As a by‐product,
Kolja Knauer, Gil Puig i Surroca
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Frequent Subgraph Mining in Outerplanar Graphs [PDF]
, 2010 In recent years there has been an increased interest in frequent pattern discovery in large databases of graph structured objects. While the frequent connected subgraph mining problem for tree datasets can be solved in incremental polynomial time, it ...
Horvath, Tamas +2 more
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Tight Distance Query Reconstruction for Trees and Graphs Without Long Induced Cycles
Random Structures &Algorithms, Volume 66, Issue 4, July 2025.ABSTRACT Given access to the vertex set V$$ V $$ of a connected graph G=(V,E)$$ G=\left(V,E\right) $$ and an oracle that given two vertices u,v∈V$$ u,v\in V $$, returns the shortest path distance between u$$ u $$ and v$$ v $$, how many queries are needed to reconstruct E$$ E $$?
Paul Bastide, Carla Groenland
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Feedback Arc Number and Feedback Vertex Number of Cartesian Product of Directed Cycles
Discrete Dynamics in Nature and Society, Volume 2019, Issue 1, 2019., 2019 For a digraph D, the feedback vertex number τ(D), (resp. the feedback arc number τ′(D)) is the minimum number of vertices, (resp. arcs) whose removal leaves the resultant digraph free of directed cycles. In this note, we determine τ(D) and τ′(D) for the Cartesian product of directed cycles D=Cn1→□Cn2→□…Cnk→. Actually, it is shown that τ′D=n1n2…nk∑i=1k1/
Xiaohong Chen +2 more
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A Universal Point Set for 2-Outerplanar Graphs
, 2015 A point set $S \subseteq \mathbb{R}^2$ is universal for a class $\cal G$ if every graph of ${\cal G}$ has a planar straight-line embedding on $S$. It is well-known that the integer grid is a quadratic-size universal point set for planar graphs, while the
C Binucci +8 more
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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
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On the Geometric Ramsey Number of Outerplanar Graphs
, 2013 We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on $2n$ vertices are bounded by $O(n^{3})$ and $O(
Cibulka, Josef +4 more
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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
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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
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