Problems on chain partitions
نویسندگان
چکیده
منابع مشابه
Chain Partitions
In the text, a proof is given of a result with a similar statement that a partially ordered set with height k is a union of k C 1 antichains (the number is k C 1 because the height of partially ordered set is the defined to be the number of links in the longest chain, and there is one more node in the chain than the number of links). The introduction to Dilworth’s Theorem claims that it has a s...
متن کاملOn-Line Chain Partitions of Orders
We analyze the on-line chain partitioning problem as a two-person game. One person builds an order one point at a time. The other person responds by making an irrevocable assignment of the new point to a chain of a chain partition. Kierstead gave a strategy showing that width k orders can be on-line chain partitioned into (5 k ?1)=4 chains. We rst prove that width two orders can be partitioned ...
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We present a few results and a larger number of questions concerning partitions of graphs or hypergraphs, where the objective is to maximize or minimize several quantities simultaneously. We consider a variety of extremal problems; many of these also have algorithmic counterparts.
متن کاملJudicious partitions and related problems
Many classical partitioning problems in combinatorics ask for a single quantity to be maximized or minimized over a set of partitions of a combinatorial object. For instance, Max Cut asks for the largest bipartite subgraph of a graphG, while Min Bisection asks for the minimum size of a cut into two equal pieces. In judicious partitioning problems, we seek to maximize or minimize a number of qua...
متن کاملOn-line Chain Partitions of Up-growing Semi-orders
On-line chain partition is a two-player game between Spoiler and Algorithm. Spoiler presents a partially ordered set, point by point. Algorithm assigns incoming points (immediately and irrevocably) to the chains which constitute a chain partition of the order. The value of the game for orders of width w is a minimum number val(w) such that Algorithm has a strategy using at most val(w) chains on...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1988
ISSN: 0012-365X
DOI: 10.1016/0012-365x(88)90204-x