منابع مشابه
Integral complete r-partite graphs
A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we give a useful sufficient and necessary condition for complete r-partite graphs to be integral, from which we can construct infinite many new classes of such integral graphs. It is proved that the problem of finding such integral graphs is equivalent to the problem of solving some Diophantin...
متن کاملOn Integral Complete R−partite Graphs
A graph G is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper we investigate integral complete r−partite graphs Kp1,p2,...,pr = Ka1p1,a2p2,...,asps with s ≤ 4. New sufficient conditions for complete 3-partite graphs and complete 4-partite graphs to be integral are given. From these conditions we construct infinitely many new classes of integral complete...
متن کاملComplete r-partite subgraphs of dense r-graphs
Let r ≥ 3 and (lnn)−1/(r−1) ≤ α ≤ r−3. We show that: Every r-uniform graph on n vertices with at least αnr/r! edges contains a complete r-partite graph with r − 1 parts of size ⌊ α (lnn)1/(r−1) ⌋ and one part of size ⌈ n1−α r−2 ⌉ . This result follows from a more general digraph version: Let U1, . . . , Ur be sets of size n, and M ⊂ U1 × · · · × Ur satisfy |M | ≥ αnr. If the integers s1, . . . ...
متن کاملCovering Complete r-Graphs with Spanning Complete r-Partite r-Graphs
An r-cut of the complete r-uniform hypergraph Kr n is obtained by partitioning its vertex set into r parts and taking all edges that meet every part in exactly one vertex. In other words it is the edge set of a spanning complete r-partite subhypergraph of Kr n. An r-cut cover is a collection of r-cuts so that each edge of K r n is in at least one of the cuts. While in the graph case r = 2 any 2...
متن کاملUnmixed $r$-partite graphs
Unmixed bipartite graphs have been characterized by Ravindra and Villarreal independently. Our aim in this paper is to characterize unmixed $r$-partite graphs under a certain condition, which is a generalization of Villarreal's theorem on bipartite graphs. Also, we give some examples and counterexamples in relevance to this subject.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2004
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(04)00159-1