Roi Krakovski

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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.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…

Integral Cayley multigraphs over Abelian and Hamiltonian groups

Extremal results regarding K6​-minors in graphs of girth at least 5

The Kelmans-Seymour conjecture for apex graphs

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