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Chromatic classes of 2-connected (n, n + 3)-graphs with at least two triangles

✍ Scribed by K.M. Koh; K.L. Teo

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
820 KB
Volume
127
Category
Article
ISSN
0012-365X

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✦ Synopsis

Let P(G) denote the chromatic polynomial of a graph G. Two graphs G and H are chromatically equivalent, written G-H, if P( G) = P( H). A graph G is chromatically unique if G z H for any graph H such that H-G. Let J? denote the class of 2-connected graphs with n vertices and n+3 edges which contain at least two triangles. It follows that if GE_% and H-G, then HER. In this paper, we determine all equivalence classes in 2 under the equivalence relation -and characterize the structure of the graphs in each class. As a by-product of these, we obtain various new families of chromatically equivalent graphs and chromatically unique graphs.

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## Abstract A point disconnecting set __S__ of a graph __G__ is a nontrivial __m__‐separator, where __m__ = |__S__|, if the connected components of __G__ ‐ __S__ can be partitioned into two subgraphs, each of which has at least two points. A 3‐connected graph is quasi 4‐connected if it has no nontr