Further characterizations and Helly-property in k-trees
DOI:
https://doi.org/10.12723/mjs.38.1Abstract
The purpose of this paper is to obtain a characterization of $k$-trees in terms of $k$-connectivity and forbidden subgraphs. Also, we present the other characterizations of $k$-trees containing the full vertices by using the join operation. Further, we establish the property of $k$-trees dealing with the degrees and formulate the Helly-property for a family of nontrivial $k$-paths in a $k$-tree. We study the planarity of $k$-trees and express the maximal outerplanar graphs in terms of 2-trees and $K_2$-neighbourhoods. Finally, the similar type of results for the maximal planar graphs are obtained.
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Copyright (c) 2016 H P Patil, Ph D
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