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Vertex-disjoint stars in graphs

100%
Ota K.
Discussiones Mathematicae Graph Theory
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2001
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tom 21
|
nr 2
179-185
EN
In this paper, we give a sufficient condition for a graph to contain vertex-disjoint stars of a given size. It is proved that if the minimum degree of the graph is at least k+t-1 and the order is at least (t+1)k + O(t²), then the graph contains k vertex-disjoint copies of a star $K_{1,t}$. The condition on the minimum degree is sharp, and there is an example showing that the term O(t²) for the number of uncovered vertices is necessary in a sense.
2
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On Super Edge-Antimagicness of Subdivided Stars

100%
Raheem A., Javaid M., Baig A. Q.
Discussiones Mathematicae Graph Theory
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2015
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tom 35
|
nr 4
663-673
EN
Enomoto, Llado, Nakamigawa and Ringel (1998) defined the concept of a super (a, 0)-edge-antimagic total labeling and proposed the conjecture that every tree is a super (a, 0)-edge-antimagic total graph. In the support of this conjecture, the present paper deals with different results on super (a, d)-edge-antimagic total labeling of subdivided stars for d ∈ {0, 1, 2, 3}.
3
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Decomposition of Complete Multigraphs Into Stars and Cycles

100%
Beggas F., Haddad M., Kheddouci H.
Discussiones Mathematicae Graph Theory
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2015
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tom 35
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nr 4
629-639
EN
Let k be a positive integer, Sk and Ck denote, respectively, a star and a cycle of k edges. λKn is the usual notation for the complete multigraph on n vertices and in which every edge is taken λ times. In this paper, we investigate necessary and sufficient conditions for the existence of the decomposition of λKn into edges disjoint of stars Sk’s and cycles Ck’s.
4
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Saturation Spectrum of Paths and Stars

100%
Faudree J., Faudree R. J., Gould R. J., Jacobson M. S., Thomas B. J.
Discussiones Mathematicae Graph Theory
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2017
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tom 37
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nr 3
811-822
EN
A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from G̅ to G results in a copy of H. The minimum size of an H-saturated graph on n vertices is denoted sat(n,H), while the maximum size is the well studied extremal number, ex(n,H). The saturation spectrum for a graph H is the set of sizes of H saturated graphs between sat(n,H) and ex(n,H). In this paper we completely determine the saturation spectrum of stars and we show the saturation spectrum of paths is continuous from sat(n, Pk) to within a constant of ex(n, Pk) when n is sufficiently large.
5
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On the Decompositions of Complete Graphs into Cycles and Stars on the Same Number of Edges

100%
Abueida A. A., Lian C.
Discussiones Mathematicae Graph Theory
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2014
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tom 34
|
nr 1
113-125
EN
Let Cm and Sm denote a cycle and a star on m edges, respectively. We investigate the decomposition of the complete graphs, Kn, into cycles and stars on the same number of edges. We give an algorithm that determines values of n, for a given value of m, where Kn is {Cm, Sm}-decomposable. We show that the obvious necessary condition is sufficient for such decompositions to exist for different values of m.
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