Unique Path Partitions: Characterization and Congruences
نویسندگان
چکیده
منابع مشابه
Congruences in ordered pairs of partitions
1. Introducing the birank. A partition is defined as being a nonincreasing sequence of positive integers, λ = (λ1,λ2, . . . ,λr ). The set of all partitions, which includes the empty partition ∅, is denoted by . The sum of the parts of a given partition is called the weight of the partition, wt(λ) = λ1+λ2+···+λr . It is standard notation to write (z;q)∞ := ∏ t≥0(1−zq) and p−k(n) for the coeffic...
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For a fixed positive integer k, the k-path partition problem is to partition the vertex set of a graph into the smallest number of paths such that each path has at most k vertices. The 2path partition problem is equivalent to the edge-cover problem. This paper presents a linear-time algorithm for the k-path partition problem in trees. The algorithm is applicable to the problem of finding the mi...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2013
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-013-0206-5