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Average degree and contractibility
Author(s) -
Kriesell Matthias
Publication year - 2006
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20131
Subject(s) - mathematics , combinatorics , graph , discrete mathematics , degree (music) , physics , acoustics
It is proved that for every number k there exists a number f ( k ) such that every finite k ‐connected graph of average degree exceeding f ( k ) contains an edge whose contraction yields again a k ‐connected graph. For the proof, tree orders on certain sets of smallest separating sets of the graph in question are constructed. This leads to new canonical tree decompositions as well. © 2005 Wiley Periodicals, Inc. J Graph Theory