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COMPLEXITY: Exercise No. 4 due in two weeks
 

Summary: COMPLEXITY: Exercise No. 4
due in two weeks
1. a. (Test 99)Is the following problem NP-complete?
Instance: A graph G = (V; E), a positive integer K.
Question: Does G contain an independent set of size K and a clique of size K?
b. Is the problem NP-complete when the K = 100?
c. Is the problem NP-complete when the K = jV j=2?
2. Show that INDEPENDENT SET remains NP-complete even if the input graph has no clique
of size 3. (Test 95)
3. Are the following problems NP-complete or polynomial? (prove)
CONNECTED DOMINATING SET:
Instance: A graph G = (V; E), positive integer K.
Question: Does G contain dominating set S with at most K vertices such that the subgraph
of G induced by S (i.e., the graph G S = (S; E \ S  S)) is connected ?
MINIMUM LEAF SPANNING TREE:
Instance: A graph G = (V; E), a positive integer K.
Question: Is there a spanning tree for G in which the number of leaves is at most K ?
MAXIMUM LEAF SPANNING TREE: (Test 95)
Instance: A graph G, a positive integer K.
Question: Is there a spanning tree for G such that the number of leaves in the tree is at least

  

Source: Azar, Yossi - School of Computer Science, Tel Aviv University

 

Collections: Computer Technologies and Information Sciences