TY - GEN

T1 - Increasing the minimum degree of a graph by contractions

AU - Golovach, Petr A.

AU - Kamiński, Marcin

AU - Paulusma, Daniël

AU - Thilikos, Dimitrios M.

PY - 2012

Y1 - 2012

N2 - The Degree Contractibility problem is to test whether a given graph G can be modified to a graph of minimum degree at least d by using at most k contractions. We prove the following three results. First, Degree Contractibility is NP-complete even when d = 14. Second, it is fixed-parameter tractable when parameterized by k and d. Third, it is W[1]-hard when parameterized by k. We also study its variant where the input graph is weighted, i.e., has some edge weighting and the contractions preserve these weights. The Weighted Degree Contractibility problem is to test if a weighted graph G can be contracted to a weighted graph of minimum weighted degree at least d by using at most k weighted contractions. We show that this problem is NP-complete and that it is fixed-parameter tractable when parameterized by k.

AB - The Degree Contractibility problem is to test whether a given graph G can be modified to a graph of minimum degree at least d by using at most k contractions. We prove the following three results. First, Degree Contractibility is NP-complete even when d = 14. Second, it is fixed-parameter tractable when parameterized by k and d. Third, it is W[1]-hard when parameterized by k. We also study its variant where the input graph is weighted, i.e., has some edge weighting and the contractions preserve these weights. The Weighted Degree Contractibility problem is to test if a weighted graph G can be contracted to a weighted graph of minimum weighted degree at least d by using at most k weighted contractions. We show that this problem is NP-complete and that it is fixed-parameter tractable when parameterized by k.

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U2 - 10.1007/978-3-642-28050-4_6

DO - 10.1007/978-3-642-28050-4_6

M3 - Conference contribution

AN - SCOPUS:84858421314

SN - 9783642280498

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 67

EP - 79

BT - Parameterized and Exact Computation - 6th International Symposium, IPEC 2011, Revised Selected Papers

T2 - 6th International Symposium on Parameterized and Exact Computation, IPEC 2011

Y2 - 6 September 2011 through 8 September 2011

ER -