A graph G is said to be H-saturated if G is H-free i.e., (G has no subgraph isomorphic to H) and adding any new edge to G creates a copy of H in G. In 1986 L. Kászonyi and Zs. Tuza considered the following problem: for given m and n find the minimum size sat(n;Pₘ) of Pₘ-saturated graph of order n. They gave the number sat(n;Pₘ) for n big enough. We deal with similar problem for bipartite graphs.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1225,
author = {Aneta Dudek and A. Pawe\l\ Wojda},
title = {Pm-saturated bipartite graphs with minimum size},
journal = {Discussiones Mathematicae Graph Theory},
volume = {24},
year = {2004},
pages = {197-211},
zbl = {1063.05072},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1225}
}
Aneta Dudek; A. Paweł Wojda. Pₘ-saturated bipartite graphs with minimum size. Discussiones Mathematicae Graph Theory, Tome 24 (2004) pp. 197-211. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1225/
[000] [1] N. Alon, An extremal problem for sets with application to graph theory, J. Combin. Theory Ser. A 40 (1985) 82-89, doi: 10.1016/0097-3165(85)90048-2.
[001] [2] B. Bollobás, Extremal Graph Theory (Academic Press, New York, 1978). | Zbl 0419.05031
[002] [3] P. Erdös, A. Hajnal, and J.W. Moon, A problem in graph theory, Amer. Math. Monthly 71 (1964) 1107-111, doi: 10.2307/2311408. | Zbl 0126.39401
[003] [4] A. Gyárfás, C.C. Rousseau, and R.H. Schelp, An extremal problem for path in bipartite graphs, J. Graph Theory 8 (1984) 83-95, doi: 10.1002/jgt.3190080109. | Zbl 0576.05031
[004] [5] L. Kászonyi and Zs. Tuza, Saturated graphs with minimal number of edges, J. Graph Theory 10 (1986) 203-210, doi: 10.1002/jgt.3190100209. | Zbl 0593.05041
[005] [6] P. Turán, Eine Extremalaufgabe aus der Graphentheorie, Math. Fiz. Lapok 48 (1941) 436-452. | Zbl 0026.26903