• Publications
  • Influence
On Metric Generators of Graphs
TLDR
Results on the detection of false coins are used to approximate the metric dimension (minimum size of a generator for the metric space defined by the distances) of some particular graphs for which the problem was known and open and the existence of connected joins in graphs can be solved in polynomial time.
Coloring the Maximal Cliques of Graphs
TLDR
It is shown that "almost" all perfect graphs are 3-clique-colorable, and exact bounds and polynomial algorithms that find the clique-chromatic number for some classes of graphs are shown and NP-completeness results for some others are proved.
Ramsey‐type results for Gallai colorings
TLDR
It is proved that in every G-coloring of Kn there exists each of the following: a monochromatic double star with at least 3n+1 4 vertices; and RG(r,K3) can be determined exactly.
Shorter tours by nicer ears: 7/5-approximation for the graph-TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs
TLDR
The key new ingredient of all algorithms is a special kind of ear-decomposition optimized using forest representations of hypergraphs that provides the lower bounds that are used to deduce the approximation ratios.
Shorter tours by nicer ears: 7/5-Approximation for the graph-TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs
TLDR
The key new ingredient of all algorithms is a special kind of ear-decomposition optimized using forest representations of hypergraphs that provides the lower bounds that are used to deduce the approximation ratios.
Improving on the 1.5-Approximation of a Smallest 2-Edge Connected Spanning Subgraph
We give a $\frac{17}{12}$-approximation algorithm for the following NP-hard problem: Given a simple undirected graph, find a 2-edge connected spanning subgraph that has the minimum number of edges.
Eight-Fifth Approximation for the Path TSP
TLDR
The approximation ratio 8/5 is proved for the metric {s, t}-path-TSP problem, and more generally for shortest connected T -joins, and the simple “Best of Many” version of Christofides’ algorithm is suggested, suggested by An, Kleinberg and Shmoys (2012.
...
1
2
3
4
5
...