311 research outputs found
Locally Optimal Load Balancing
This work studies distributed algorithms for locally optimal load-balancing:
We are given a graph of maximum degree , and each node has up to
units of load. The task is to distribute the load more evenly so that the loads
of adjacent nodes differ by at most .
If the graph is a path (), it is easy to solve the fractional
version of the problem in communication rounds, independently of the
number of nodes. We show that this is tight, and we show that it is possible to
solve also the discrete version of the problem in rounds in paths.
For the general case (), we show that fractional load balancing
can be solved in rounds and discrete load
balancing in rounds for some function , independently of the
number of nodes.Comment: 19 pages, 11 figure
Spectral radius and k-factor-critical graphs
For a nonnegative integer , a graph is said to be -factor-critical
if admits a perfect matching for any with . In
this article, we prove spectral radius conditions for the existence of
-factor-critical graphs. Our result generalises one previous result on
perfect matchings of graphs. Furthermore, we claim that the bounds on spectral
radius in Theorem 3.1 are sharp.Comment: 12 page
Signless Laplacian spectral radius for a k-extendable graph
Let and be two nonnegative integers with (mod 2), and let
be a graph of order with a 1-factor. Then is said to be
-extendable for if every matching in of size
can be extended to a 1-factor. In this paper, we first establish a lower
bound on the signless Laplacian spectral radius of to ensure that is
-extendable. Then we create some extremal graphs to claim that all the
bounds derived in this article are sharp.Comment: 11 page
Spanning k-trees and distance spectral radius in graphs
Let be an integer. A tree is called a -tree if
for each , that is, the maximum degree of a -tree is at most .
Let denote the distance spectral radius in , where
denotes the distance matrix of . In this paper, we verify a upper bound for
in a connected graph to guarantee the existence of a
spanning -tree in .Comment: 11 page
- …