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National Repository of Grey Literature 3 records found  Search took 0.01 seconds. 
Beyond the Erdős–Sós conjecture
 Davoodi, Akbar ; Piguet, Diana ; Řada, Hanka ; Sanhueza-Matamala, N.
We prove an asymptotic version of a tree-containment conjecture of Klimošová, Piguet and Rozhoň [European J. Combin. 88 (2020), 103106] for graphs with quadratically many edges. The result implies that the asymptotic version of the Erdős-Sós conjecture in the setting of dense graphs is correct.
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Sufficient conditions for embedding trees
 Rozhoň, Václav ; Klimošová, Tereza (advisor) ; Dvořák, Zdeněk (referee)
We study sufficient degree conditions that force a host graph to contain a given class of trees. This setting involves some well-known problems from the area of extremal graph theory. The most famous one is the Erdős-Sós conjecture that asserts that every graph with average degree greater than k − 1 contains any tree on k + 1 vertices. Our two main results are the following. We prove an approximate version of the Erdős-Sós conjecture for dense graphs and trees with sublinear max- imum degree. We also study a natural refinement of the Loebl-Komlós-Sós conjecture and prove it is approximately true for dense graphs. Both results are based on the so-called regularity method. The second mentioned result is a joint work with T. Klimošová and D. Piguet. 1
Detailed record
Sufficient conditions for embedding trees
 Rozhoň, Václav ; Klimošová, Tereza (advisor) ; Dvořák, Zdeněk (referee)
We study sufficient degree conditions that force a host graph to contain a given class of trees. This setting involves some well-known problems from the area of extremal graph theory. The most famous one is the Erdős-Sós conjecture that asserts that every graph with average degree greater than k − 1 contains any tree on k + 1 vertices. Our two main results are the following. We prove an approximate version of the Erdős-Sós conjecture for dense graphs and trees with sublinear max- imum degree. We also study a natural refinement of the Loebl-Komlós-Sós conjecture and prove it is approximately true for dense graphs. Both results are based on the so-called regularity method. The second mentioned result is a joint work with T. Klimošová and D. Piguet. 1
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