Geodesic
Spanning trees with many leaves
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part II, Tome 381 (2010), pp. 78-87
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Let maximal chain of vertices of degree 2 in the graph $G$ consists of $k>0$ vertices. We prove that $G$ has a spanning tree with more than $\frac{v(G)}{2k+4}$ leaves (we denote by $v(G)$ the number of vertices of the graph $G$). We present an infinite serie of examples showing that the constant $\frac1{2k+4}$ cannot be enlarged. Bibl. 7 titles. 
@article{ZNSL_2010_381_a3,
     author = {D. V. Karpov},
     title = {Spanning trees with many leaves},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {78--87},
     year = {2010},
     volume = {381},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_381_a3/}
}
TY  - JOUR
AU  - D. V. Karpov
TI  - Spanning trees with many leaves
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2010
SP  - 78
EP  - 87
VL  - 381
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2010_381_a3/
LA  - ru
ID  - ZNSL_2010_381_a3
ER  - 
%0 Journal Article
%A D. V. Karpov
%T Spanning trees with many leaves
%J Zapiski Nauchnykh Seminarov POMI
%D 2010
%P 78-87
%V 381
%U http://geodesic.mathdoc.fr/item/ZNSL_2010_381_a3/
%G ru
%F ZNSL_2010_381_a3
D. V. Karpov. Spanning trees with many leaves. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part II, Tome 381 (2010), pp. 78-87. http://geodesic.mathdoc.fr/item/ZNSL_2010_381_a3/

[1] J. A. Storer, “Constructing full spanning trees for cubic graphs”, Inform. Process. Lett., 13:1 (1981), 8–11 | DOI | MR | Zbl

[2] J. R. Griggs, M. Wu, “Spanning trees in graphs of minimum degree 4 or 5”, Discrete Math., 104 (1992), 167–183 | DOI | MR | Zbl

[3] D. J. Kleitman, D. B. West, “Spanning trees with many leaves”, SIAM J. Discrete Math., 4:1 (1991), 99–106 | DOI | MR | Zbl

[4] N. Alon, “Transversal numbers of uniform hypergraphs”, Graphs and Combinatorics, 6 (1990), 1–4 | DOI | MR | Zbl

[5] N. V. Gravin, “Postroenie ostovnogo dereva grafa s bolshim kolichestvom listev”, Zap. nauchn. semin. POMI, 381, 2010, 31–46

[6] D. V. Karpov, “Ostovnoe derevo s bolshim kolichestvom visyachikh vershin”, Diskretnaya matematika, 13:1 (2001), 63–72 | DOI | MR | Zbl

[7] F. Harary, Graph theory, 1969 | MR | MR