Geodesic
On \((K_{q},k)\) stable graphs with small \(k\)
Jean-Luc Fouquet1 ; Henri Thuillier1 ; Jean-Marie Vanherpe1 ; Adam Paweł Wojda2
1LIFO - University of Orleans - France
2AGH University of Science and Technology Krakow -Poland
The electronic journal of combinatorics, Tome 19 (2012) no. 2
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A graph $G$ is $(K_{q},k)$ stable if it contains a copy of $K_{q}$ after deleting any subset of $k$ vertices. In a previous paper we have characterized the $(K_q,k)$ stable graphs with minimum size for $3 \le q \le 5$ and we have proved that the only $(K_q,k)$ stable graph with minimum size is $K_{q+k}$ for $q \ge 5$ and $k \le 3$. We show that for $q \ge 6$ and $k \le \frac{q}{2}+1$ the only $(K_q,k)$ stable graph with minimum size is isomorphic to $K_{q+k}$.
DOI : 10.37236/2435
Classification : 05C35, 05C75, 05C99
Mots-clés : stable graphs

Jean-Luc Fouquet  1   ; Henri Thuillier  1   ; Jean-Marie Vanherpe  1   ; Adam Paweł Wojda  2

1 LIFO - University of Orleans - France
2 AGH University of Science and Technology Krakow -Poland 
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     author = {Jean-Luc Fouquet and Henri Thuillier and Jean-Marie Vanherpe and Adam Pawe{\l} Wojda},
     title = {On {\((K_{q},k)\)} stable graphs with small \(k\)},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {2},
     doi = {10.37236/2435},
     zbl = {1252.05091},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2435/}
}
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Jean-Luc Fouquet; Henri Thuillier; Jean-Marie Vanherpe; Adam Paweł Wojda. On \((K_{q},k)\) stable graphs with small \(k\). The electronic journal of combinatorics, Tome 19 (2012) no. 2. doi: 10.37236/2435

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