On some path problems on oriented hypergraphs
S. Nguyen, D. Pretolani, L. Markenzon (1998)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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S. Nguyen, D. Pretolani, L. Markenzon (1998)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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Knor, M. (1995)
Acta Mathematica Universitatis Comenianae. New Series
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Mustapha Chellali, Teresa W. Haynes, Lutz Volkmann (2010)
Discussiones Mathematicae Graph Theory
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Let k be a positive integer and G = (V(G),E(G)) a graph. A subset S of V(G) is a k-independent set of G if the subgraph induced by the vertices of S has maximum degree at most k-1. The maximum cardinality of a k-independent set of G is the k-independence number βₖ(G). A graph G is called β¯ₖ-stable if βₖ(G-e) = βₖ(G) for every edge e of E(G). First we give a necessary and sufficient condition for β¯ₖ-stable graphs. Then we establish four equivalent conditions for β¯ₖ-stable trees. ...
Farrell, E.J., Wahid, S.A. (1987)
International Journal of Mathematics and Mathematical Sciences
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Levit, Vadim E., Mândrescu, Eugen (2005)
Acta Universitatis Apulensis. Mathematics - Informatics
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J.L. Fouquet, H. Thuillier, J.M. Vanherpe, A.P. Wojda (2013)
Discussiones Mathematicae Graph Theory
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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...
Ferdinand Gliviak, Martin Knor, Ľubomír Šoltés (1995)
Mathematica Slovaca
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Knor, M., Niepel, L., Olts, L. (1992)
Acta Mathematica Universitatis Comenianae. New Series
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Conte, Donatello, Foggia, Pasquale, Vento, Mario (2007)
Journal of Graph Algorithms and Applications
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