TY  - JOUR
ID  - Nikodem2015
LB  - Nikodem2015
AU  - Nikodem, Mateusz
TI  - On vertex stability of complete k-partite graphs
ST  - On vertex stability of complete k-partite graphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2015
VL  - 35
IS  - 6
SP  - 907
EP  - 914
DO  - http://dx.doi.org/10.7494/OpMath.2015.35.6.907
UR  - http://dx.doi.org/10.7494/OpMath.2015.35.6.907
AB  - Let \(H\) be any graph. We say that graph \(G\) is \(H\)-stable if \(G-u\) contains a subgraph isomorphic to \(H\) for an arbitrary chosen \(u\in V(G)\). We characterize all \(H\)-stable graphs of minimal size where \(H\) is any complete \(k\)-partite graph. Thus, we generalize the results of Dudek and Żak regarding complete bipartite graphs.
KW  - vertex stability
KW  - minimal stable graphs
KW  - complete \(k\)-partite graphs
SN  - 1232-9274
ER  -