Packing triangles in low degree graphs and indifference graphs
Copyright policy )Packing triangles in low degree graphs and indifference graphs
We consider the problems of finding the maximum number of vertex-disjoint triangles (VTP) and edge-disjoint triangles (ETP) in a simple graph. Both problems are NP-hard. The algorithm with the best approximation guarantee known so far for these problems has ratio $3/2 + ɛ$, a result that follows from a more general algorithm for set packing obtained by Hurkens and Schrijver in 1989. We present improvements on the approximation ratio for restricted cases of VTP and ETP that are known to be APX-hard: we give an approximation algorithm for VTP on graphs with maximum degree 4 with ratio slightly less than 1.2, and for ETP on graphs with maximum degree 5 with ratio 4/3. We also present an exact linear-time algorithm for VTP on the class of indifference graphs.
- Universidade de São Paulo Brazil
- UNIVERSIDADE DE SAO PAULO Brazil
Low degree graph, low degree graph, Polynomial algorithm, [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], polynomial algorithm, Indifference graph, Approximation algorithm, Approximation algorithms, Theoretical Computer Science, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Graph algorithms (graph-theoretic aspects), QA1-939, indifference graph, Discrete Mathematics and Combinatorics, packing triangles, triangle packing, Packing triangles, Mathematics, approximation algorithm, [math.math-co] mathematics [math]/combinatorics [math.co]
Low degree graph, low degree graph, Polynomial algorithm, [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], polynomial algorithm, Indifference graph, Approximation algorithm, Approximation algorithms, Theoretical Computer Science, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Graph algorithms (graph-theoretic aspects), QA1-939, indifference graph, Discrete Mathematics and Combinatorics, packing triangles, triangle packing, Packing triangles, Mathematics, approximation algorithm, [math.math-co] mathematics [math]/combinatorics [math.co]
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