Results 31 to 40 of about 875,640 (148)

On edge-group choosability of graphs [PDF]

, 2011
In this paper, we study the concept of edge-group choosability of graphs. We say that G is edge k-group choosable if its line graph is k-group choosable. An edge-group choosability version of Vizing conjecture is given.
Khamseh, Amir, Omidi, Gholamreza
core  

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 node-capacitated Okamura-Seymour theorem

, 2012
The classical Okamura-Seymour theorem states that for an edge-capacitated, multi-commodity flow instance in which all terminals lie on a single face of a planar graph, there exists a feasible concurrent flow if and only if the cut conditions are ...
Lee, James R., Mendel, Manor, Moharrami, Mohammad   +2 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, 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

Long induced paths in graphs

, 2016
We prove that every 3-connected planar graph on $n$ vertices contains an induced path on $\Omega(\log n)$ vertices, which is best possible and improves the best known lower bound by a multiplicative factor of $\log \log n$.
Esperet, Louis, Lemoine, Laetitia, Maffray, Frédéric   +2 more
core   +3 more sources

Classical Ising model test for quantum circuits

, 2009
We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically.
Aharonov D Arad I Eban E Landau Z, Barahona F, Bernstein E, Bravyi S, Bravyi S, Chartrand G, Daniel A Lidar, Dawson C M, De las Cuevas G Dür W Van den Nest M Briegel H J, Gross J, Jané E, Jerrum M R Sinclair A, Joseph Geraci, Jozsa R, Jozsa R Miyake A, Kassal I Jordan S P Love P J Mohseni M Aspuru-Guzik A, Kasteleyn P W, Kitaev A Yu, Knill E, Lidar D A, Markov I L Shi Y, Meyer D A, Mezard M, Nielsen M A, Perdomo A Truncik C Tubert-Brohman I Rose G Aspuru-Guzik A, Reichl L E, Shor P W Jordan S P, Van den Nest M Dür W Raussendorf R Briegel H J, Welsh D J A, Wiegers M, Wiesner S   +30 more
core   +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
semanticscholar   +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  

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., Komusiewicz, Christian, Niedermeier, Rolf, Sorge, Manuel, van Bevern, René   +4 more
core