Roi Krakovski

activity

20102016

most citedConflict-Free Coloring Made Stronger

11 citations · 16 across the 7 of their papers we have counts for

collaborators

Showing math.COShow all

6 papers · 1 filter

math.CO2014

Homological face-width condition forcing $K_{6}$ -minors in graphs on surfaces

Roi Krakovski, Bojan Mohar

It is proved that every graph embedded on a (non-spherical) surface with non-separating face-width at least $7$ contains a minor isomorphic to $K_{6}$ . It is also shown that face-wid…

math.CO2012★ 1 cited

Integral Cayley multigraphs over Abelian and Hamiltonian groups

Matt DeVos, Roi Krakovski, Bojan Mohar +1

It is shown that a Cayley multigraph over a group $G$ with generating multiset $S$ is integral (i.e., all of its eigenvalues are integers) if $S$ lies in the integral cone over the…

math.CO2012★ 1 cited

Spectrum of Cayley graphs on the symmetric group generated by transpositions

Roi Krakovski, Bojan Mohar

For an integer $n \geq 2$ , let $X_{n}$ be the Cayley graph on the symmetric group $S_{n}$ generated by the set of transpositions $(12), (13), ..., (1 n)$ . It is shown that the spectrum…

math.CO2010

Extremal results regarding $K_{6}$ -minors in graphs of girth at least 5

Elad Aigner-Horev, Roi Krakovski

We prove that every 6-connected graph of girth $\geq 6$ has a $K_{6}$ -minor and thus settle the Jorgensen conjecture for graphs of girth $\geq 6$ . Relaxing the assumption on the gir…

math.CO2010

The Kelmans-Seymour conjecture for apex graphs

Elad Aigner-Horev, Roi Krakovski

We provide a short proof that a 5-connected nonplanar apex graph contains a subdivided $K_{_{5}}$ or a $K_{_{4}}^{-}$ (= $K_{_{4}}$ with a single edge removed) as a subgraph. Together with…

math.CO2010★ 11 cited

Conflict-Free Coloring Made Stronger

Elad Horev, Roi Krakovski, Shakhar Smorodinsky

In FOCS 2002, Even et al. showed that any set of $n$ discs in the plane can be Conflict-Free colored with a total of at most $O (lo g n)$ colors. That is, it can be colored with $O(…