Chenyu Yan

Collective tree spanners of graphs

In this paper we introduce a new notion of collective tree spanners. We say that a graph G=(V,E)admits a system of

Spanners for bounded tree-length graphs

\mu

Additive spanners for k-chordal graphs

collective additive tree r-spanners if there is a system T(G) of at most

Additive sparse spanners for graphs with bounded length of largest induced cycle

\mu

Collective tree 1-spanners for interval graphs

spanning trees of G such that for any two vertices x,y of G a spanning tree T\in \cT(G) exists such that d_T(x,y)\leq d_G(x,y)+r. Among other results, we show that any chordal graph, chordal bipartite graph or cocomparability graph admits a system of at most log2n collective additive tree 2-spanners. These results are complemented by lower bounds, which say that any system of collective additive tree 1-spanners must have

Collective tree spanners in graphs with bounded genus, chordality, tree-width, or clique-width

\Omega(\sqrt{n})

Collective Tree Spanners of Graphs

spanning trees for some chordal graphs and

Collective Tree Spanners in Graphs with Bounded Parameters

\Omega(n)

Compact and Low Delay Routing Labeling Scheme for Unit Disk Graphs

spanning trees for some chordal bipartite graphs and some cocomparability graphs. Furthermore, we show that any c-chordal graph admits a system of at most log2n collective additive tree (2\lfloor c/2\rfloor)-spanners, any circular-arc graph admits a system of two collective additive tree 2-spanners. Towards establishing these results, we present a general property for graphs, called (\al,r)

Network flow spanners

-decomposition, and show that any