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# Paloma T. Lima, Graph Square Roots of Small Distance from Degree One Graphs

## Wednesday, July 22, 2020 @ 4:30 PM - 5:30 PM KST

Zoom ID: 869 4632 6610 (ibsdimag)

### Speaker

Paloma T. Lima
Department of Computer Science, University of Bergen
http://www.ii.uib.no/~palomal/

Given a graph class $\mathcal{H}$, the task of the $\mathcal{H}$-Square Root problem is to decide whether an input graph G has a square root H that belongs to $\mathcal{H}$. We are interested in the parameterized complexity of the problem for classes $\mathcal{H}$ that are composed by the graphs at vertex deletion distance at most $k$ from graphs of maximum degree at most one. That is, we are looking for a square root H that has a modulator S of size k such that H-S is the disjoint union of isolated vertices and disjoint edges. We show that different variants of the problems with constraints on the number of isolated vertices and edges in H-S are FPT when parameterized by k, by providing algorithms with running time $2^{2^{O(k)}}\cdot n^{O(1)}$. We further show that the running time of our algorithms is asymptotically optimal and it is unlikely that the double-exponential dependence on k could be avoided. In particular, we prove that the VC-k Root problem, that asks whether an input graph has a square root with vertex cover of size at most k, cannot be solved in time $2^{2^{o(k)}}\cdot n^{O(1)}$ unless the Exponential Time Hypothesis fails. Moreover, we point out that VC-k Root parameterized by k does not admit a subexponential kernel unless P=NP.

This is a joint work with Petr Golovach and Charis Papadopoulos.

## Details

Date:
Wednesday, July 22, 2020
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:

## Venue

Zoom ID: 869 4632 6610 (ibsdimag)

## Organizer

O-joung Kwon (권오정)
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209