Geodesic
T-irreducible extensions for starlike trees
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 3, pp. 330-339

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We deal with a sort of optimal extensions of graphs, so called T-irreducible extensions. T-irreducible extension of a graph $G$ is an extension of $G$ obtained by removing a maximal set of edges from the trivial extension of $G$. A difficult starlike tree is a starlike tree that has at least one difficult node. T-irreducible extensions for nondifficult starlike trees were constructed by M. B. Abrosimov, T-irreducible extensions for palms (one of subclasses of starlike trees) were constructed by S. G. Kurnosova. Counterexamples were found to a method of Harary and Khurum, who tried to construct possible T-irreducible extensions for starlike trees. T-irreducible extensions for difficult starlike trees are constructed. 
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     author = {D. Yu. Osipov},
     title = {T-irreducible extensions for starlike trees},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {330--339},
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D. Yu. Osipov. T-irreducible extensions for starlike trees. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 3, pp. 330-339. http://geodesic.mathdoc.fr/item/ISU_2015_15_3_a11/