We say that a graphical invariant i of a graph interpolates over a family 8 of graphs if i satisfies the following property: If rn and M are the minimum and maximum values (respectively) of i over all graphs in 8 then for each k , rn 4 k I M , there is a graph H in 8 for which i ( H ) = k . In previ
Interpolation theorems for a family of spanning subgraphs
β Scribed by Sanming Zhou
- Book ID
- 110419615
- Publisher
- Springer
- Year
- 1998
- Tongue
- English
- Weight
- 403 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0011-4642
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At the 4th International Graph Theory Conference (1980), G. Chartrand posed the following problem: If a (connected) graph G contains spanning trees with m and n pendant vertices, respectively, with m < n, does G contain a spanning tree with k pendant vertices for every integer k, where m<k<n? Recent
## Abstract Let __p__ β₯ __2__ be a fixed integer. Let __G__ be a simple and 2βedgeβconnected graph on __n__ vertices, and let __g__ be the girth of __G.__ If __d__(__u__) + __d__(__v__) β₯ (__2__/(__g β 2__))((__n/p__) β 4 + __g__) holds whenever __uv__ β __E__(__G__), and if __n__ is sufficiently l
## Abstract The following interpolation theorem is proved: If a graph __G__ contains spanning trees having exactly __m__ and __n__ endβvertices, with __m__ < __n__, then for every integer __k, m < k < n, G__ contains a spanning tree having exactly __k__ endβvertices. This settles a problem posed by