Results 71 to 80 of about 3,901 (159)
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
A graph and its complement with specified properties I: connectivity
International Journal of Mathematics and Mathematical Sciences, 1979 We investigate the conditions under which both a graph G and its complement G¯ possess a specified property. In particular, we characterize all graphs G for which G and G¯ both (a) have connectivity one, (b) have line-connectivity one, (c) are 2 ...
Jin Akiyama, Frank Harary
doaj +1 more source
, 2012 It is shown that for any outerplanar graph G there is a one to one mapping of the vertices of G to the plane, so that the number of distinct distances between pairs of connected vertices is at most three. This settles a problem of Carmi, Dujmovic, Morin and Wood.
Alon, Noga, Feldheim, Ohad Noy
openaire +2 more sources
Vertex-Coloring with Star-Defects
, 2016 Defective coloring is a variant of traditional vertex-coloring, according to which adjacent vertices are allowed to have the same color, as long as the monochromatic components induced by the corresponding edges have a certain structure.
A Edelman +19 more
core +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
Outerplanar Partitions of Planar Graphs
Journal of Combinatorial Theory, Series B, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
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
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
Scaling Limits of Random Graphs from Subcritical Classes: Extended abstract [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We study the uniform random graph $\mathsf{C}_n$ with $n$ vertices drawn from a subcritical class of connected graphs. Our main result is that the rescaled graph $\mathsf{C}_n / \sqrt{n}$ converges to the Brownian Continuum Random Tree $\mathcal{T}_ ...
Konstantinos Panagiotou +2 more
doaj +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