## Abstract

Graph product is a fundamental tool with rich applications in both graph theory and theoretical computer science. It is usually studied in the form f(G * H) where G and H are graphs, * is a graph product and f is a graph property. For example, if f is the independence number and * is the disjunctive product, then the product is known to be multiplicative: f(G * H) = f(G)f(H). In this paper, we study graph products in the following non-standard form: f((G⊕H)*J) where G, H and J are graphs, ⊕ and * are two different graph products and f is a graph property. We show that if f is the induced and semi-induced matching number, then for some products ⊕ and *, it is subadditive in the sense that f((G⊕H) * J) ≤ f(G * J) + f(H * J). Moreover, when f is the poset dimension number, it is almost subadditive. As applications of this result (we only need J = K_{2} here), we obtain tight hardness of approximation for various problems in discrete mathematics and computer science: bipartite induced and semi-induced matching (a.k.a. maximum expanding sequences), poset dimension, maximum feasible subsystem with 0/1 coefficients, unit-demand min-buying and single-minded pricing, donation center location, boxicity, cubicity, threshold dimension and independent packing.

Original language | English |
---|---|

Title of host publication | Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013 |

Pages | 1557-1576 |

Number of pages | 20 |

Publication status | Published - 2013 |

MoE publication type | A4 Article in a conference publication |

Event | ACM-SIAM Symposium on Discrete Algorithms - New Orleans, United States Duration: 6 Jan 2013 → 8 Jan 2013 Conference number: 24 |

### Conference

Conference | ACM-SIAM Symposium on Discrete Algorithms |
---|---|

Abbreviated title | SODA |

Country/Territory | United States |

City | New Orleans |

Period | 06/01/2013 → 08/01/2013 |