Results 71 to 80 of about 161 (144)

Genus Distributions of 4-Regular Outerplanar Graphs [PDF]

The Electronic Journal of Combinatorics, 2011
We present an $O(n^2)$-time algorithm for calculating the genus distribution of any 4-regular outerplanar graph. We characterize such graphs in terms of what we call split graphs and incidence trees. The algorithm uses post-order traversal of the incidence tree and productions that are adapted from a previous paper that analyzes double-root vertex ...
Poshni, Mehvish I., Khan, Imran F., Gross, Jonathan L.   +2 more
openaire   +2 more sources

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, Linda Cook, Meike Hatzel, Claire Hilaire, Freddie Illingworth, Rose McCarty   +5 more
wiley   +1 more source

The product structure of squaregraphs

Journal of Graph Theory, Volume 105, Issue 2, Page 179-191, February 2024.
Abstract A squaregraph is a plane graph in which each internal face is a 4‐cycle and each internal vertex has degree at least 4. This paper proves that every squaregraph is isomorphic to a subgraph of the semistrong product of an outerplanar graph and a path.
Robert Hickingbotham, Paul Jungeblut, Laura Merker, David R. Wood   +3 more
wiley   +1 more source

Crosscap of the non-cyclic graph of groups

AKCE International Journal of Graphs and Combinatorics, 2016
The non-cyclic graph CG to a non locally cyclic group G is as follows: take G∖Cyc(G) as vertex set, where Cyc(G)={x∈G|〈x,y〉  is cyclic for all  y∈G} is called the cyclicizer of G, and join two vertices if they do not generate a cyclic subgroup.
K. Selvakumar, M. Subajini
doaj   +1 more source

On the Intersection Graphs Associeted to Posets

Discussiones Mathematicae - General Algebra and Applications, 2020
Let (P, ≤) be a poset with the least element 0. The intersection graph of ideals of P, denoted by G(P), is a graph whose vertices are all nontrivial ideals of P and two distinct vertices I and J are adjacent if and only if I ∩ J ≠ {0}.
Afkhami M., Khashyarmanesh K., Shahsavar F.   +2 more
doaj   +1 more source

The Cayley Sum Graph of Ideals of a Lattice

Discussiones Mathematicae - General Algebra and Applications, 2020
Let L be a lattice, 𝒥(L) be the set of ideals of L and S be a subset of 𝒥 (L). In this paper, we introduce an undirected Cayley graph of L, denoted by ΓL,S with elements of 𝒥 (L) as the vertex set and, for two distinct vertices I and J, I is adjacent to ...
Afkhami Mojgan, Hassankhani Mehdi, Khashyarmanesh Kazem   +2 more
doaj   +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

Planar linear arrangements of outerplanar graphs

IEEE Transactions on Circuits and Systems, 1988
Given an n-vertex outerplanar graph G, we consider the problem of arranging the vertices of G on a line such that no two edges cross and various cost measures are minimized. We present efficient algorithms for generating layouts in which every edge (i,j) of G does not exceed a given bandwidth b(i,j), the total edge length and the cutwidth of the layout
Frederickson, Greg N., Hambrusch, Susanne E.   +1 more
openaire   +3 more sources

On Separating Path and Tree Systems in Graphs [PDF]

Discrete Mathematics & Theoretical Computer Science
We explore the concept of separating systems of vertex sets of graphs. A separating system of a set $X$ is a collection of subsets of $X$ such that for any pair of distinct elements in $X$, there exists a set in the separating system that contains ...
Ahmad Biniaz, Prosenjit Bose, Jean-Lou De Carufel, Anil Maheshwari, Babak Miraftab, Saeed Odak, Michiel Smid, Shakhar Smorodinsky, Yelena Yuditsky   +8 more
doaj   +1 more source

DEFICIENCY OF OUTERPLANAR GRAPHS

Proceedings of the YSU A: Physical and Mathematical Sciences, 2017
An edge-coloring of a graph G with colors $1,2,...,t$ is an interval $t$-coloring, if all colors are used, and the colors of edges incident to each vertex of $G$ are distinct and form an interval of integers. A graph $G$ is interval colorable, if it has an interval $t$-coloring for some positive integer $t$.
openaire   +1 more source