The local cover
The local cover is a new object designed to model the local structure of a graph. I wrote a survey explaining the local cover.
Posts by Tags
expository writing
graph-decompositions
What do bags of decompositions represent?
One main aim of my work on local-global decompositions is to define a graph width parameter which captures precisely when a graph has dense local structure. Width in this context is the maximum size of a bag of a certain kind of graph-decomposition. So, for notions of “local width” to succeed, bags of decompositions must interact in some way with local dense structures. But how, exactly?
The right definition of decomposition, part II
In a previous post, I discussed some reasons why I like the definition of graph-decomposition. But why do I care about graph-decompositions to begin with? In this post, I go deeper into what I hope graph-decompositions can do.
The right definition of decomposition
Graph-decompositions are defined by taking the definition of tree-decomposition, crossing out “tree”, and writing “graph” instead. Is this the right definition?
local cover
The local cover
The local cover is a new object designed to model the local structure of a graph. I wrote a survey explaining the local cover.
local-global
What do bags of decompositions represent?
One main aim of my work on local-global decompositions is to define a graph width parameter which captures precisely when a graph has dense local structure. Width in this context is the maximum size of a bag of a certain kind of graph-decomposition. So, for notions of “local width” to succeed, bags of decompositions must interact in some way with local dense structures. But how, exactly?
The right definition of decomposition, part II
In a previous post, I discussed some reasons why I like the definition of graph-decomposition. But why do I care about graph-decompositions to begin with? In this post, I go deeper into what I hope graph-decompositions can do.
The local cover
The local cover is a new object designed to model the local structure of a graph. I wrote a survey explaining the local cover.
Locally chordal graphs
My paper on locally chordal graphs appeared on arXiv! (See also: a recent talk I gave about this topic.) I’m very happy about this paper! In this post, I try to explain why.
new paper
Locally chordal graphs
My paper on locally chordal graphs appeared on arXiv! (See also: a recent talk I gave about this topic.) I’m very happy about this paper! In this post, I try to explain why.