Results 1 to 10 of about 1,620,998 (201)

The Odd Chromatic Number of a Planar Graph is at Most 8 [PDF]

Graphs and Combinatorics, 2022
Petruševski and Škrekovski recently introduced the notion of an odd colouring of a graph: a proper vertex colouring of a graph G is said to be odd if for each non-isolated vertex $$x \in V(G)$$ x ∈ V ( G ) there exists a colour c appearing an odd number ...
J. Petr, Julien Portier
semanticscholar   +1 more source

The structure and the list 3-dynamic coloring of outer-1-planar graphs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2021
An outer-1-planar graph is a graph admitting a drawing in the plane so that all vertices appear in the outer region of the drawing and every edge crosses at most one other edge.
Yan Li, Xin Zhang
doaj   +1 more source

An improved planar graph product structure theorem [PDF]

Electronic Journal of Combinatorics, 2021
Dujmović, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every planar graph $G$ there is a graph $H$ with treewidth at most 8 and a path $P$ such that $G\subseteq H\boxtimes P$. We improve this result by replacing "treewidth at most
T. Ueckerdt, D. Wood, Wendy Yi
semanticscholar   +1 more source

Improved product structure for graphs on surfaces [PDF]

Discrete Mathematics & Theoretical Computer Science, 2022
Dujmovi\'c, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every graph $G$ with Euler genus $g$ there is a graph $H$ with treewidth at most 4 and a path $P$ such that $G\subseteq H \boxtimes P \boxtimes K_{\max\{2g,3\}}$. We improve
Marc Distel, Robert Hickingbotham, Tony Huynh, David R. Wood   +3 more
doaj   +1 more source

Shallow Minors, Graph Products, and Beyond-Planar Graphs [PDF]

SIAM Journal on Discrete Mathematics, 2021
The planar graph product structure theorem of Dujmovi\'{c}, Joret, Micek, Morin, Ueckerdt, and Wood [J. ACM 2020] states that every planar graph is a subgraph of the strong product of a graph with bounded treewidth and a path.
Robert Hickingbotham, D. Wood
semanticscholar   +1 more source

Quantum approximate optimization of non-planar graph problems on a planar superconducting processor [PDF]

Nature Physics, 2020
Faster algorithms for combinatorial optimization could prove transformative for diverse areas such as logistics, finance and machine learning. Accordingly, the possibility of quantum enhanced optimization has driven much interest in quantum technologies.
F. Arute, K. Arya, R. Babbush, D. Bacon, J. Bardin, R. Barends, S. Boixo, M. Broughton, B. Buckley, D. Buell, B. Burkett, N. Bushnell, Yu Chen, Zijun Chen, B. Chiaro, R. Collins, W. Courtney, S. Demura, A. Dunsworth, E. Farhi, A. Fowler, B. Foxen, C. Gidney, M. Giustina, R. Graff, S. Habegger, M. Harrigan, A. Ho, Sabrina Hong, Trent Huang, L. Ioffe, S. Isakov, E. Jeffrey, Zhang Jiang, Cody Jones, D. Kafri, K. Kechedzhi, J. Kelly, Seon Kim, P. Klimov, A. Korotkov, F. Kostritsa, D. Landhuis, P. Laptev, Mike Lindmark, M. Leib, E. Lucero, O. Martin, J. Martinis, J. McClean, M. McEwen, A. Megrant, X. Mi, M. Mohseni, W. Mruczkiewicz, J. Mutus, O. Naaman, M. Neeley, C. Neill, F. Neukart, H. Neven, M. Niu, T. O’Brien, B. O’Gorman, E. Ostby, A. Petukhov, Harald Putterman, C. Quintana, P. Roushan, N. Rubin, D. Sank, K. Satzinger, Andrea Skolik, V. Smelyanskiy, D. Strain, Michael Streif, Kevin J Sung, M. Szalay, A. Vainsencher, T. White, Z. Yao, P. Yeh, Adam Zalcman, Leo Zhou   +83 more
semanticscholar   +1 more source

DiGress: Discrete Denoising diffusion for graph generation [PDF]

International Conference on Learning Representations, 2022
This work introduces DiGress, a discrete denoising diffusion model for generating graphs with categorical node and edge attributes. Our model utilizes a discrete diffusion process that progressively edits graphs with noise, through the process of adding ...
Clément Vignac, Igor Krawczuk, Antoine Siraudin, Bohan Wang, V. Cevher, P. Frossard   +5 more
semanticscholar   +1 more source

Non-Separating Planar Graphs [PDF]

The Electronic Journal of Combinatorics, 2021
A graph $G$ is a non-separating planar graph if there is a drawing $D$ of $G$ on the plane such that (1) no two edges cross each other in $D$ and (2) for any cycle $C$ in $D$, any two vertices not in $C$ are on the same side of $C$ in $D$. Non-separating planar graphs are closed under taking minors and are a subclass of planar graphs and a superclass ...
Dehkordi, Hooman R., Farr, Graham
openaire   +2 more sources

Planar Legendrian graphs

Algebraic & Geometric Topology, 2022
We prove two results on the classification of trivial Legendrian embeddings $g: G \rightarrow (S^3, _{std})$ of planar graphs. First, the oriented Legendrian ribbon $R_g$ and rotation invariant $\text{rot}_g$ are a complete set of invariants. Second, if $G$ is 3-connected or contains $K_4$ as a minor, then the unique trivial embedding of $G$ is ...
Lambert-Cole, Peter, O'Donnol, Danielle
openaire   +2 more sources

On the planarity of line Mycielskian graph of a graph

Ratio Mathematica, 2020
The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤  i ≤  q and e, then for 1 ≤  i ≤  q , joining ei' to the neighbours of ei  and  to e.
Keerthi G. Mirajkar, Anuradha V Deshpande   +1 more
doaj   +1 more source