Neighborhood conditions for balanced independent sets in bipartite graphs

نویسندگان

  • Denise Amar
  • Stephan Brandt
  • Daniel Brito
  • Oscar Ordaz
چکیده

Let G be a balanced bipartite graph of order 2n and minimum degree (G) 3. If for every balanced independent set S of four vertices in G the neighborhood union jN(S)j > n then G is traceable, the circumference is at least 2n ? 2 and G contains a 2-factor (with one exceptional graph for the latter statement). If jN(S)j > n + 2 then G is hamiltonian.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Balanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations

A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...

متن کامل

Different-Distance Sets in a Graph

A set of vertices $S$ in a connected graph $G$ is a different-distance set if, for any vertex $w$ outside $S$, no two vertices in $S$ have the same distance to $w$.The lower and upper different-distance number of a graph are the order of a smallest, respectively largest, maximal different-distance set.We prove that a different-distance set induces either a special type of path or an independent...

متن کامل

Maximal independent sets in bipartite graphs with at least one cycle

A maximal independent set is an independent set that is not a proper subset of any other independent set. Liu [J.Q. Liu, Maximal independent sets of bipartite graphs, J. Graph Theory, 17 (4) (1993) 495-507] determined the largest number of maximal independent sets among all n-vertex bipartite graphs. The corresponding extremal graphs are forests. It is natural and interesting for us to consider...

متن کامل

A generalization of Villarreal's result for unmixed tripartite graphs

‎In this paper we give a characterization of unmixed tripartite‎ ‎graphs under certain conditions which is a generalization of a‎ ‎result of Villarreal on bipartite graphs‎. ‎For bipartite graphs two‎ ‎different characterizations were given by Ravindra and Villarreal‎. ‎We show that these two characterizations imply each other‎.

متن کامل

Neighborhood Reconstruction and Cancellation of Graphs

We connect two seemingly unrelated problems in graph theory. Any graph G has a neighborhood multiset N (G) = {N(x) | x ∈ V (G)} whose elements are precisely the open vertex-neighborhoods of G. In general there exist non-isomorphic graphs G and H for which N (G) = N (H). The neighborhood reconstruction problem asks the conditions under which G is uniquely reconstructible from its neighborhood mu...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discrete Mathematics

دوره 181  شماره 

صفحات  -

تاریخ انتشار 1998