scholarly journals An exponential time parameterized algorithm for planar disjoint paths

Author(s):  
Daniel Lokshtanov ◽  
Pranabendu Misra ◽  
Michał Pilipczuk ◽  
Saket Saurabh ◽  
Meirav Zehavi
1999 ◽  
Vol 197-198 (1-3) ◽  
pp. 285-298 ◽  
Author(s):  
D Ferrero
Keyword(s):  

1992 ◽  
Vol 57 (6) ◽  
pp. 1326-1334 ◽  
Author(s):  
Jaroslav Vojtěchovský ◽  
Jindřich Hašek ◽  
Stanislav Nešpůrek ◽  
Mojmír Adamec

2,4,4,6-Tetraphenyl-4H-thiopyran, C29H22S, orthorhombic, Pna21, a = 17.980(4), b = 6.956(2), c = 34.562(11) Å, V = 4323(2) Å3, Z = 8, Dx = 1.237 g cm-3, F(000) = 1696, λ(CuKα) = 1.54184 A, μ = 1.372 mm-2, T = 294 K. The final R was 0.050 for the unique set of 3103 observed reflections. The central 4H-thiopyran ring forms a boat conformation for both symmetrically independent molecules with average boat angles 4.4(3) and 6.8(3)° at S and C(sp3), respectively. The mean planes of phenyls at the position 2 and 6 are turned from the double plane of 4H-thiopyran by 42.5(5) and 35.8(3)°, respectively. The investigated material undergoes a photochromic change in the solid state after irradiation with UV light or X-rays. The maximum of the new absorption band is situated at 564 nm. The non-exponential time dependence of photochromic bleaching is analysed in terms of a dispersive first-order reaction.


2020 ◽  
Vol 31 (4) ◽  
pp. 703-711 ◽  
Author(s):  
Niu Liqiang ◽  
Xie Yongjun ◽  
Jiang Haolin ◽  
Wu Peiyu

Author(s):  
Vytautas Gruslys ◽  
Shoham Letzter

Abstract Magnant and Martin conjectured that the vertex set of any d-regular graph G on n vertices can be partitioned into $n / (d+1)$ paths (there exists a simple construction showing that this bound would be best possible). We prove this conjecture when $d = \Omega(n)$ , improving a result of Han, who showed that in this range almost all vertices of G can be covered by $n / (d+1) + 1$ vertex-disjoint paths. In fact our proof gives a partition of V(G) into cycles. We also show that, if $d = \Omega(n)$ and G is bipartite, then V(G) can be partitioned into n/(2d) paths (this bound is tight for bipartite graphs).


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