Recursively arbitrarily vertex-decomposable graphs | Zendy

Olivier Baudon | Zendy; Frédéric Gilbert | Zendy; Mariusz Woźniak | Zendy

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Recursively arbitrarily vertex-decomposable graphs

Author(s) -

Olivier Baudon,

Frédéric Gilbert,

Mariusz Woźniak

Publication year - 2012

Publication title -

opuscula mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 16

eISSN - 2300-6919

pISSN - 1232-9274

DOI - 10.7494/opmath.2012.32.4.689

Subject(s) - combinatorics , vertex (graph theory) , suns in alchemy , mathematics , disjoint sets , discrete mathematics , sequence (biology) , cograph , graph , pathwidth , line graph , physics , optoelectronics , biology , genetics

A graph \(G = (V;E)\) is arbitrarily vertex decomposable if for any sequence \(\tau\) of positive integers adding up to \(|V|\), there is a sequence of vertex-disjoint subsets of \(V\) whose orders are given by \(\tau\), and which induce connected graphs. The main aim of this paper is to study the recursive version of this problem. We present a solution for trees, suns, and partially for a class of 2-connected graphs called balloons

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