7 research outputs found
Packing internally disjoint Steiner paths of data center networks
Let and denote the maximum number of
edge-disjoint paths in a graph such that
for any and . If
, then is the maximum number of edge-disjoint spanning
paths in . It is proved [Graphs Combin., 37 (2021) 2521-2533] that deciding
whether is NP-complete for a given . For an
integer with , the -path connectivity of a graph is
defined as min and , which
is a generalization of tree connectivity. In this paper, we study the -path
connectivity of the -dimensional data center network with -port switches
which has significate role in the cloud computing, and prove that
with and
Sets as graphs
The aim of this thesis is a mutual transfer of computational and structural results and techniques between sets and graphs. We study combinatorial enumeration of sets, canonical encodings, random generation, digraph immersions. We also investigate the underlying structure of sets in algorithmic terms, or in connection with hereditary graphs classes. Finally, we employ a set-based proof-checker to verify two classical results on claw-free graph