Graphic sequences with a realization containing a generalized friendship graph

Gould, Jacobson and Lehel [R.J. Gould, M.S. Jacobson, J. Lehel, Potentially G-graphical degree sequences, in: Y. Alavi, et al. (Eds.), Combinatorics, Graph Theory and Algorithms, vol. I, New Issues Press, Kalamazoo, MI, 1999, pp. 451–460] considered a variation of the classical Turán-type extremal p...

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Bibliographic Details
Published in:Discrete mathematics Vol. 308; no. 24; pp. 6226 - 6232
Main Authors: Yin, Jian-Hua, Chen, Gang, Schmitt, John R.
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 28.12.2008
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Degree sequence
Exact sciences and technology
Generalized friendship graph
Graph theory
Information retrieval. Graph
Mathematics
Potentially [formula omitted]-graphic sequence
Sciences and techniques of general use
Theoretical computing
Potentially F t , r , k -graphic sequence
Generalized friendship graph
Degree sequence
Integer
Graphics
Algorithm theory
Complete graph
Subgraph
Graph theory
Combinatorics
Potentially Ft,r,k-graphic sequence
Graph algorithm
ISSN:0012-365X, 1872-681X
Online Access:Get full text
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Summary:Gould, Jacobson and Lehel [R.J. Gould, M.S. Jacobson, J. Lehel, Potentially G-graphical degree sequences, in: Y. Alavi, et al. (Eds.), Combinatorics, Graph Theory and Algorithms, vol. I, New Issues Press, Kalamazoo, MI, 1999, pp. 451–460] considered a variation of the classical Turán-type extremal problems as follows: for any simple graph H , determine the smallest even integer σ ( H , n ) such that every n -term graphic sequence π = ( d 1 , d 2 , … , d n ) with term sum σ ( π ) = d 1 + d 2 + ⋯ + d n ≥ σ ( H , n ) has a realization G containing H as a subgraph. Let F t , r , k denote the generalized friendship graph on k t − k r + r vertices, that is, the graph of k copies of K t meeting in a common r set, where K t is the complete graph on t vertices and 0 ≤ r ≤ t . In this paper, we determine σ ( F t , r , k , n ) for k ≥ 2 , t ≥ 3 , 1 ≤ r ≤ t − 2 and n sufficiently large.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2007.11.075