Results 41 to 50 of about 1,772 (132)

On reconstructing maximal outerplanar graphs

Discrete Mathematics, 1974
Manvel has proved that a maximal outerplanar graph can be reconstructed from the collection of isomorphism types of subgraphs obtained by deleting vertices of the given graph. This paper sharpens Manvel's result by showing that if the graph is not a triangulation of a hexagon, then reconstruction can be accomplished using only those isomorphism types ...
openaire   +1 more source

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
wiley   +1 more source

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, Baoyindureng Wu, Seenith Sivasundaram   +2 more
wiley   +1 more source

A Survey of Maximal k-Degenerate Graphs and k-Trees

Theory and Applications of Graphs
This article surveys results on maximal $k$-degenerate graphs, $k$-trees, and related classes including simple $k$-trees, $k$-paths, maximal outerplanar graphs, and Apollonian networks.
Allan Bickle
doaj   +1 more source

Crossing Minimization for 1-page and 2-page Drawings of Graphs with Bounded Treewidth

, 2014
We investigate crossing minimization for 1-page and 2-page book drawings. We show that computing the 1-page crossing number is fixed-parameter tractable with respect to the number of crossings, that testing 2-page planarity is fixed-parameter tractable ...
Bannister, Michael J., Eppstein, David
core   +1 more source

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
wiley   +1 more source

Geometric Assortative Growth Model for Small‐World Networks

The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014
It has been shown that both humanly constructed and natural networks are often characterized by small‐world phenomenon and assortative mixing. In this paper, we propose a geometrically growing model for small‐world networks. The model displays both tunable small‐world phenomenon and tunable assortativity.
Yilun Shang, H. M. Chamberlin, Y. Zhang
wiley   +1 more source

Fuzzy Outerplanar Graphs and Its Applications

International Journal of Computational Intelligence Systems
The concept of a crisp graph is essential in the study of outerplanar graphs because outerplanar graphs are a unique type of planar graphs containing special characteristics. One of the core concepts of crisp graphs, the notion of a subgraph, is utilized
Deivanai Jaisankar, Sujatha Ramalingam, Nagarajan Deivanayagampillai, Tadesse Walelign   +3 more
doaj   +1 more source

Total domination in maximal outerplanar graphs

Discrete Applied Mathematics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dorfling, Michael, Hattingh, Johannes H., Jonck, Elizabeth   +2 more
openaire   +1 more source

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