Discussiones Mathematicae Graph Theory 33(1) (2013) 9-23
doi: 10.7151/dmgt.1654

Dedicated to the 70th Birthday of Mieczysław Borowiecki

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

Kinnari Amin

Department of Mathematics, Computer Science, and Engineering
Georgia Perimeter College
Clarkston, GA 30021

Jill Faudree

Department of Mathematics and Statistics
University of Alaska Fairbanks
Fairbanks, AK 99775-6660

Ronald J. Gould

Department of Mathematics and Computer Science
Emory University
Atlanta, GA 30322

Elżbieta Sidorowicz

Faculty of Mathematics, Computer Science and Econometrics
University of Zielona Góra
Szafrana 4a, 65--516 Zielona Góra, Poland

Abstract

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: for which values of n and m are there any n-vertex maximal Kp-free graphs of size m?

Keywords: extremal problems, maximal Kp-free graphs, Kp-saturated graphs

2010 Mathematics Subject Classification: 05C35.

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Received 3 July 2012
Revised 22 October 2012
Accepted 23 October 2012