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Tree representations of graphs

European Journal of Combinatorics, ISSN: 0195-6698, Vol: 28, Issue: 4, Page: 1087-1098
2007
  • 4
    Citations
  • 2
    Usage
  • 3
    Captures
  • 0
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

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Article Description

A graph is chordal if and only if it is the intersection graph of some family of subtrees of a tree. Applying “tolerance” allows larger families of graphs to be represented by subtrees. A graph G is in the family [Δ,d,t] if there is a tree with maximum degree Δ and subtrees corresponding to the vertices of G such that each subtree has maximum degree at most d and two vertices of G are adjacent if and only if the subtrees corresponding to them have at least t common vertices.

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