4,572 research outputs found

    Some results on triangle partitions

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    We show that there exist efficient algorithms for the triangle packing problem in colored permutation graphs, complete multipartite graphs, distance-hereditary graphs, k-modular permutation graphs and complements of k-partite graphs (when k is fixed). We show that there is an efficient algorithm for C_4-packing on bipartite permutation graphs and we show that C_4-packing on bipartite graphs is NP-complete. We characterize the cobipartite graphs that have a triangle partition

    Distinguishing partitions of complete multipartite graphs

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    A \textit{distinguishing partition} of a group XX with automorphism group aut(X){aut}(X) is a partition of XX that is fixed by no nontrivial element of aut(X){aut}(X). In the event that XX is a complete multipartite graph with its automorphism group, the existence of a distinguishing partition is equivalent to the existence of an asymmetric hypergraph with prescribed edge sizes. An asymptotic result is proven on the existence of a distinguishing partition when XX is a complete multipartite graph with m1m_1 parts of size n1n_1 and m2m_2 parts of size n2n_2 for small n1n_1, m2m_2 and large m1m_1, n2n_2. A key tool in making the estimate is counting the number of trees of particular classes
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