Perfect pairs of trees in graphs | Zendy

Novak Ladislav | Zendy; Gibbons Alan | Zendy

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Perfect pairs of trees in graphs

Author(s) -

Novak Ladislav,

Gibbons Alan

Publication year - 1992

Publication title -

international journal of circuit theory and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.364

H-Index - 52

eISSN - 1097-007X

pISSN - 0098-9886

DOI - 10.1002/cta.4490200206

Subject(s) - symmetrization , mathematics , lemma (botany) , generalization , graph , combinatorics , discrete mathematics , perfect graph theorem , relation (database) , line graph , computer science , pathwidth , ecology , mathematical analysis , poaceae , database , biology

We introduce the concept of perfect pairs of trees of a graph as a natural generalization of so‐called maximally distant pairs of trees. Several propositions and remarks are presented to display the properties of this new notion. Lemma 1, which plays a central role, gives five equivalent statements characterizing the relation ‘to be maximally distant from’ between pairs of trees. Symmetrization of this relation leads to our concept of a perfect pair of trees, the properties of which are given in Theorem 1. Remark 4 shows how naturally our new concept arises. Additionally, certain examples are provided to illustrate perfect pair structures in a graph.

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