# Pₘ-saturated bipartite graphs with minimum size

Discussiones Mathematicae Graph Theory (2004)

- Volume: 24, Issue: 2, page 197-211
- ISSN: 2083-5892

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topAneta Dudek, and A. Paweł Wojda. "Pₘ-saturated bipartite graphs with minimum size." Discussiones Mathematicae Graph Theory 24.2 (2004): 197-211. <http://eudml.org/doc/270410>.

@article{AnetaDudek2004,

abstract = {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.},

author = {Aneta Dudek, A. Paweł Wojda},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {graph; saturated graph; extremal graph; bipartite graph},

language = {eng},

number = {2},

pages = {197-211},

title = {Pₘ-saturated bipartite graphs with minimum size},

url = {http://eudml.org/doc/270410},

volume = {24},

year = {2004},

}

TY - JOUR

AU - Aneta Dudek

AU - A. Paweł Wojda

TI - Pₘ-saturated bipartite graphs with minimum size

JO - Discussiones Mathematicae Graph Theory

PY - 2004

VL - 24

IS - 2

SP - 197

EP - 211

AB - 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.

LA - eng

KW - graph; saturated graph; extremal graph; bipartite graph

UR - http://eudml.org/doc/270410

ER -

## References

top- [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.
- [2] B. Bollobás, Extremal Graph Theory (Academic Press, New York, 1978). Zbl0419.05031
- [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. Zbl0126.39401
- [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. Zbl0576.05031
- [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. Zbl0593.05041
- [6] P. Turán, Eine Extremalaufgabe aus der Graphentheorie, Math. Fiz. Lapok 48 (1941) 436-452. Zbl0026.26903

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