On the non-(p-1)-partite Kp-free graphs

نویسندگان

  • Kinnari Amin
  • Jill R. Faudree
  • Ronald J. Gould
  • Elzbieta Sidorowicz
چکیده

We say that a graph G is maximal Kp-free if G does not contain Kp but if we add any new edge e ∈ E(G) to G, then the graph G+ e contains Kp. We study the minimum and maximum size of non-(p − 1)-partite maximal Kp-free graphs with n vertices. We also answer the interpolation question: Unauthenticated Download Date | 2/2/17 7:37 PM 10 K. Amin, J. Faudree, R.J. Gould and E. Sidorowicz for which values of n and m are there any n-vertex maximal Kp-free graphs of size m?

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

Some Algebraic and Combinatorial Properties of the Complete $T$-Partite Graphs

In this paper, we characterize the shellable complete $t$-partite graphs. We also show for these types of graphs the concepts vertex decomposable, shellable and sequentially Cohen-Macaulay are equivalent. Furthermore, we give a combinatorial condition for the Cohen-Macaulay complete $t$-partite graphs.

متن کامل

Unmixed $r$-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.

متن کامل

A proof of the stability of extremal graphs, Simonovits' stability from Szemerédi's regularity

The following sharpening of Turán’s theorem is proved. Let Tn,p denote the complete p– partite graph of order n having the maximum number of edges. If G is an n-vertex Kp+1-free graph with e(Tn,p) − t edges then there exists an (at most) p-chromatic subgraph H0 such that e(H0) ≥ e(G)− t. Using this result we present a concise, contemporary proof (i.e., one using Szemerédi’s regularity lemma) fo...

متن کامل

ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS

Let $G$ be a non-abelian finite group. In this paper, we prove that $Gamma(G)$ is $K_4$-free if and only if $G cong A times P$, where $A$ is an abelian group, $P$ is a $2$-group and $G/Z(G) cong mathbb{ Z}_2 times mathbb{Z}_2$. Also, we show that $Gamma(G)$ is $K_{1,3}$-free if and only if $G cong {mathbb{S}}_3,~D_8$ or $Q_8$.

متن کامل

An Extremal Problem On Potentially Kr+1-H-graphic Sequences

A sequence S is potentially Kp,1,1 graphical if it has a realization containing a Kp,1,1 as a subgraph, where Kp,1,1 is a complete 3-partite graph with partition sizes p, 1, 1. Let σ(Kp,1,1, n) denote the smallest degree sum such that every n-term graphical sequence S with σ(S) ≥ σ(Kp,1,1, n) is potentially Kp,1,1 graphical. In this paper, we prove that σ(Kp,1,1, n) ≥ 2[((p + 1)(n − 1) + 2)/2] ...

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:
  • Discussiones Mathematicae Graph Theory

دوره 33  شماره 

صفحات  -

تاریخ انتشار 2013