On Minimum (Kq, K) Stable Graphs

• Autorzy: J.L. Fouquet , H. Thuillier , J.M. Vanherpe , A.P. Wojda
• Języki publikacji: EN

Abstrakty

EN

A graph G is a (Kq, k) stable graph (q ≥ 3) if it contains a Kq after deleting any subset of k vertices (k ≥ 0). Andrzej ˙ Zak in the paper On (Kq; k)-stable graphs, ( doi:/10.1002/jgt.21705) has proved a conjecture of Dudek, Szyma´nski and Zwonek stating that for sufficiently large k the number of edges of a minimum (Kq, k) stable graph is (2q − 3)(k + 1) and that such a graph is isomorphic to sK2q−2 + tK2q−3 where s and t are integers such that s(q − 1) + t(q − 2) − 1 = k. We have proved (Fouquet et al. On (Kq, k) stable graphs with small k, Elektron. J. Combin. 19 (2012) #P50) that for q ≥ 5 and k ≤ q 2 +1 the graph Kq+k is the unique minimum (Kq, k) stable graph. In the present paper we are interested in the (Kq, k(q)) stable graphs of minimum size where k(q) is the maximum value for which for every nonnegative integer k

Słowa kluczowe

EN

stable graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 1
• Strony: 101-115

Daty

wydano

2013-03-01

online

2013-04-13

Twórcy

autor

J.L. Fouquet

• L.I.F.O., Faculté des Sciences, B.P. 6759 Université d’Orléans, 45067 Orléans Cedex 2, France

autor

H. Thuillier

• L.I.F.O., Faculté des Sciences, B.P. 6759 Université d’Orléans, 45067 Orléans Cedex 2, France

autor

J.M. Vanherpe

• L.I.F.O., Faculté des Sciences, B.P. 6759 Université d’Orléans, 45067 Orléans Cedex 2, France

autor

A.P. Wojda

• Wydzia l Matematyki Stosowanej Zak lad Matematyki Dyskretnej A.G.H., Al. Mickiewicza 30, 30-059 Kraków, Poland

Bibliografia

• [1] J.A. Bondy and U.S.R. Murty, Graph Theory, 244 ( Springer, Series Graduate Texts in Mathematics, 2008).
• [2] A. Dudek, A. Szymański and M. Zwonek, (H, k) stable graphs with minimum size, Discuss. Math. Graph Theory 28 (2008) 137-149. doi:10.7151/dmgt.1397[Crossref]
• [3] J.-L. Fouquet, H. Thuillier, J.-M. Vanherpe and A.P. Wojda, On (Kq, k) stable graphs with small k, Electron. J. Combin. 19 (2012) #P50.
• [4] J.-L. Fouquet, H. Thuillier, J.-M. Vanherpe and A.P. Wojda, On (Kq, k) vertex stable graphs with minimum size, Discrete Math. 312 (2012) 2109-2118. doi:10.1016/j.disc.2011.04.017[WoS][Crossref]
• [5] P. Frankl and G.Y. Katona, Extremal k-edge-hamiltonian hypergraphs, Discrete Math. 308 (2008) 1415-1424. doi:10.1016/j.disc.2007.07.074[WoS][Crossref]
• [6] G.Y. Katona and I. Horváth, Extremal P4-stable graphs, Discrete Appl. Math. 159 (2011) 1786-1792. doi:10.1016/j.dam.2010.11.016[Crossref]
• [7] J.J. Sylvester, Question 7382, Mathematical Questions from the Educational Times, (1884) 41:21.
• [8] A. Żak, On (Kq; k)-stable graphs, J. Graph Theory, (2012),to appear. doi:/10.1002/jgt.21705

Identyfikatory

DOI

10.7151/dmgt.1656