Unmixed $r$-partite graphs
نویسندگان
چکیده مقاله:
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.
منابع مشابه
Factors of r-partite graphs
We give sufficient conditions for a tripartite graph to have a spanning subgraph consisting of complete graphs of order 3. This is applied to bound the strong chromatic number of a graph.
متن کاملRainbow Matchings in r-Partite r-Graphs
Given a collection of matchings M = (M1,M2, . . . ,Mq) (repetitions allowed), a matching M contained in ⋃ M is said to be s-rainbow for M if it contains representatives from s matchings Mi (where each edge is allowed to represent just one Mi). Formally, this means that there is a function φ : M → [q] such that e ∈ Mφ(e) for all e ∈ M , and |Im(φ)| > s. Let f(r, s, t) be the maximal k for which ...
متن کاملIntegral 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 کاملPerfect matchings in r-partite r-graphs
Let H be an r-partite r-graph, all of whose sides have the same size n. Suppose that there exist two sides of H , each satisfying the following condition: the degree of each legal r−1-tuple contained in the complement of this side is strictly larger than n 2 . We prove that under this condition H must have a perfect matching. This answers a question of Kühn and Osthus.
متن کاملCohen-Macaulay $r$-partite graphs with minimal clique cover
In this paper, we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is Cohen-Macaulay. It is proved that if there exists a cover of an $r$-partite Cohen-Macaulay graph by disjoint cliques of size $r$, then such a cover is unique.
متن کاملIndependent transversals in r-partite graphs
Let G(r, n) denote the set of all r-partite graphs consisting of n vertices in each partite class. An independent transversal of G ∈ G(r, n) is an independent set consisting of exactly one vertex from each vertex class. Let ∆(r, n) be the maximal integer such that every G ∈ G(r, n) with maximal degree less than ∆(r, n) contains an independent transversal. Let Cr = limn→∞ ∆(r,n) n . We establish...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 43 شماره 3
صفحات 781- 787
تاریخ انتشار 2017-06-01
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
کلمات کلیدی
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023