Unmixed $r$-partite graphs

Authors

  • R. Jafarpour-Golzari Department of Mathematics‎, ‎Institute for Advanced Studies‎ ‎in Basic Science (IASBS)‎, ‎P.O‎. ‎Box 45195-1159‎, ‎Zanjan‎, ‎Iran.}
  • R. Zaare-Nahandi Department of Mathematics‎, ‎Institute for Advanced Studies‎ ‎in Basic Science (IASBS)‎, ‎P.O‎. ‎Box 45195-1159‎, ‎Zanjan‎, ‎Iran.
Abstract:

‎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.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

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.

full text

Rainbow 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 ...

full text

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...

full text

Perfect 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.

full text

Cohen-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.

full text

Independent 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...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 43  issue 3

pages  781- 787

publication date 2017-06-01

{@ msg @}

By following a journal you will be notified via email when a new issue of this journal is published.

Keywords

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023