P.A. Golovach
How to eliminate a graph
Golovach, P.A.; Heggernes, P.; van 't Hof, P.; Manne, F.; Paulusma, D.; Pilipczuk, M.
Authors
P. Heggernes
P. van 't Hof
F. Manne
Professor Daniel Paulusma daniel.paulusma@durham.ac.uk
Professor
M. Pilipczuk
Contributors
Martin Charles Golumbic
Editor
Michal Stern
Editor
Avivit Levy
Editor
Gila Morgenstern
Editor
Abstract
Vertex elimination is a graph operation that turns the neighborhood of a vertex into a clique and removes the vertex itself. It has widely known applications within sparse matrix computations. We define the Elimination problem as follows: given two graphs G and H, decide whether H can be obtained from G by |V(G)| − |V(H)| vertex eliminations. We study the parameterized complexity of the Elimination problem. We show that Elimination is W[1]-hard when parameterized by |V(H)|, even if both input graphs are split graphs, and W[2]-hard when parameterized by |V(G)| − |V(H)|, even if H is a complete graph. On the positive side, we show that Elimination admits a kernel with at most 5|V(H)| vertices in the case when G is connected and H is a complete graph, which is in sharp contrast to the W[1]-hardness of the related Clique problem. We also study the case when either G or H is tree. The computational complexity of the problem depends on which graph is assumed to be a tree: we show that Elimination can be solved in polynomial time when H is a tree, whereas it remains NP-complete when G is a tree.
Presentation Conference Type | Conference Paper (Published) |
---|---|
Publication Date | 2012 |
Deposit Date | Mar 11, 2013 |
Pages | 320-331 |
Series Title | Lecture notes in computer science |
Series Number | 7551 |
Series ISSN | 0302-9743,1611-3349 |
Book Title | Graph-theoretic concepts in computer science: 38th international workshop, WG 2012, Jerusalem, Israel, June 26-28, 2012, revised selected papers. |
ISBN | 9783642346101 |
DOI | https://doi.org/10.1007/978-3-642-34611-8_32 |
Public URL | https://durham-repository.worktribe.com/output/1156186 |
Additional Information | Series: Lecture Notes in Computer Science, Volume 7551 |
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