Directed paths in a random potential

1991 ◽  
Vol 43 (13) ◽  
pp. 10728-10742 ◽  
Author(s):  
Daniel S. Fisher ◽  
David A. Huse
Keyword(s):  
Random Potential ◽  
Directed Paths

On the propagator related to an electron in a random potential

1988 ◽  
Vol 21 (8) ◽  
pp. L451-L454
Author(s):  
A B Nassar ◽  
J M F Bassalo ◽  
H S Antunes Neto ◽  
P T S Alencar
Keyword(s):  
Random Potential

Kinetics in a Random Potential

2018 ◽  
pp. 165-198
Author(s):  
Jørgen Rammer
Keyword(s):  
Random Potential

scholarly journals Linial's Dual Conjecture for Path-Spine Digraphs

2020 ◽  
Author(s):  
Vinícius De Souza Carvalho ◽  
Cândida Nunes Da Silva ◽  
Orlando Lee
Keyword(s):  
Stable Sets ◽  
Hamilton Path ◽  
Directed Paths ◽  
Vertex Disjoint ◽  
Single Path

 Given a digraph D, a coloring 𝒞 of D is a partition of V(D) into stable sets. The k-norm of 𝒞 is defined as ΣC∈𝒞 min{|C|, k}. A coloring of D with minimum k-norm has its k-norm noted by χk(D). A (path)-k-pack of a digraph D is a set of k vertex-disjoint (directed) paths of D. The weight of a k-pack is the number of vertices covered by the k-pack. We denote by λk(D) the weight of a maximum k-pack. Linial conjectured that χk(D) ≤ λk(D) for every digraph. Such conjecture remains open, but has been proved for some classes of digraphs. We prove the conjecture for path-spine digraphs, defined as follows. A digraph D is path-spine if there exists a partition {X, Y} of V(D) such that D[X] has a Hamilton path and every arc in D[Y] belongs to a single path Q. 

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