Results 81 to 90 of about 3,509 (176)
A note on zero-divisor graph of amalgamated duplication of a ring along an ideal
AKCE International Journal of Graphs and Combinatorics, 2017 Let be a commutative ring and be a non-zero ideal of . Let be the subring of consisting of the elements for and . In this paper we characterize all isomorphism classes of finite commutative rings with identity and ideal such that is planar.
A. Mallika, R. Kala
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
The role of twins in computing planar supports of hypergraphs
, 2020 A support or realization of a hypergraph $H$ is a graph $G$ on the same vertex as $H$ such that for each hyperedge of $H$ it holds that its vertices induce a connected subgraph of $G$.
Kanj, Iyad A. +4 more
core
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 +3 more
wiley +1 more source
To Prove Four Color Theorem [PDF]
, 2016 In this paper, we give a proof for four color theorem(four color conjecture). Our proof does not involve computer assistance and the most important is that it can be generalized to prove Hadwiger Conjecture. Moreover, we give algorithms to color and test
Cao, Weiwei, Yue, Weiya
core
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. +2 more
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. +1 more
openaire +3 more sources
A Survey of Maximal k-Degenerate Graphs and k-Trees
Theory and Applications of GraphsThis 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
, 2013 We introduce a notion of bipartite minors and prove a bipartite analog of Wagner's theorem: a bipartite graph is planar if and only if it does not contain $K_{3,3}$ as a bipartite minor.
Chudnovsky, Maria +4 more
core +1 more source