(H,k) stable graphs with minimum size

Aneta Dudek; Artur Szymański; Małgorzata Zwonek

Discussiones Mathematicae Graph Theory (2008)

  • Volume: 28, Issue: 1, page 137-149
  • ISSN: 2083-5892

Abstract

top
Let us call a G (H,k) graph vertex stable if it contains a subgraph H ever after removing any of its k vertices. By Q(H,k) we will denote the minimum size of an (H,k) vertex stable graph. In this paper, we are interested in finding Q(₃,k), Q(₄,k), Q ( K 1 , p , k ) and Q(Kₛ,k).

How to cite

top

Aneta Dudek, Artur Szymański, and Małgorzata Zwonek. "(H,k) stable graphs with minimum size." Discussiones Mathematicae Graph Theory 28.1 (2008): 137-149. <http://eudml.org/doc/270227>.

@article{AnetaDudek2008,
abstract = {Let us call a G (H,k) graph vertex stable if it contains a subgraph H ever after removing any of its k vertices. By Q(H,k) we will denote the minimum size of an (H,k) vertex stable graph. In this paper, we are interested in finding Q(₃,k), Q(₄,k), $Q(K_\{1,p\},k)$ and Q(Kₛ,k).},
author = {Aneta Dudek, Artur Szymański, Małgorzata Zwonek},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph; stable graph; stable graphs; minimum size; cycles; complete graphs},
language = {eng},
number = {1},
pages = {137-149},
title = {(H,k) stable graphs with minimum size},
url = {http://eudml.org/doc/270227},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Aneta Dudek
AU - Artur Szymański
AU - Małgorzata Zwonek
TI - (H,k) stable graphs with minimum size
JO - Discussiones Mathematicae Graph Theory
PY - 2008
VL - 28
IS - 1
SP - 137
EP - 149
AB - Let us call a G (H,k) graph vertex stable if it contains a subgraph H ever after removing any of its k vertices. By Q(H,k) we will denote the minimum size of an (H,k) vertex stable graph. In this paper, we are interested in finding Q(₃,k), Q(₄,k), $Q(K_{1,p},k)$ and Q(Kₛ,k).
LA - eng
KW - graph; stable graph; stable graphs; minimum size; cycles; complete graphs
UR - http://eudml.org/doc/270227
ER -

References

top
  1. [1] P. Frankl and G.Y. Katona, Extremal k-edge-hamiltonian hypergraphs, accepted for publication in Discrete Math. Zbl1182.05089
  2. [2] I. Horváth and G.Y. Katona, Extremal stable graphs, manuscript. Zbl1228.05187
  3. [3] R. Greenlaw and R. Petreschi, Cubic Graphs, ACM Computing Surveys, No. 4, (1995). 

NotesEmbed ?

top

You must be logged in to post comments.