The median problem on k-partite graphs
نویسندگان
چکیده
منابع مشابه
The median problem on k-partite graphs
In a connected graph G, the status of a vertex is the sum of the distances of that vertex to each of the other vertices in G. The subgraph induced by the vertices of minimum (maximum) status in G is called the median (anti-median) of G. The median problem of graphs is closely related to the optimization problems involving the placement of network servers, the core of the entire networks. Bipart...
متن کاملOn finding k-cliques in k-partite graphs
In this paper, a branch-and-bound algorithm for finding all cliques of size k in a kpartite graph is proposed that improves upon the method of Grunert et al (2002). The new algorithm uses bit-vectors, or bitsets, as the main data structure in bit-parallel operations. Bitsets enable a new form of data representation that improves branching and backtracking of the branch-and-bound procedure. Nume...
متن کاملThe Zarankiewicz problem in 3-partite graphs
Let F be a graph, k ≥ 2 be an integer, and write exχ≤k(n, F ) for the maximum number of edges in an n-vertex graph that is k-partite and has no subgraph isomorphic to F . The function exχ≤2(n, F ) has been studied by many researchers. Finding exχ≤2(n,Ks,t) is a special case of the Zarankiewicz problem. We prove an analogue of the Kövári-Sós-Turán Theorem by showing exχ≤3(n,Ks,t) ≤ ( 1 3 )1−1/s(...
متن کاملScore Sets in Oriented k - partite Graphs
Let D(U1, U2, ..., Uk) be an oriented k -partite graph with |Ui| = ni, 1 ≤ i ≤ k. Then, the score of a vertex ui in Ui is defined by aui (or simply ai ) = ∑k t=1, t 6=i nt+d + ui −d − ui , where d+ui and d − ui are respectively the outdegree and indegree of ui. The set A of distinct scores of the vertices of D(U1, U2, ..., Uk) is called its score set. In this paper, we prove that if a1 is a non...
متن کاملSpanners of Complete k -Partite Geometric Graphs
We address the following problem: Given a complete k-partite geometric graph K whose vertex set is a set of n points in R, compute a spanner of K that has a “small” stretch factor and “few” edges. We present two algorithms for this problem. The first algorithm computes a (5 + )-spanner of K with O(n) edges in O(n log n) time. The second algorithm computes a (3 + )-spanner of K with O(n log n) e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2015
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1802