On Sufficient Conditions for Hamiltonicity in Dense Graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00581997" target="_blank" >RIV/67985807:_____/21:00581997 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/978-3-030-83823-2_85" target="_blank" >https://doi.org/10.1007/978-3-030-83823-2_85</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-83823-2_85" target="_blank" >10.1007/978-3-030-83823-2_85</a>

Result language
angličtina
Original language name
On Sufficient Conditions for Hamiltonicity in Dense Graphs
Original language description
We study structural conditions in dense graphs that guarantee the existence of vertex-spanning substructures such as Hamilton cycles. Recall that every Hamiltonian graph is connected, has an almost perfect matching and, excluding the bipartite case, contains an odd cycle. Our main result states that any large enough graph that robustly satisfies these properties must already be Hamiltonian. Moreover, the same holds for powers of cycles and the bandwidth setting subject to natural generalizations of connectivity, matchings and odd cycles. This solves the embedding problem that underlies multiple lines of research on sufficient conditions for Hamiltonicity. As an application, we recover several old and new results, and prove versions of the Bandwidth Theorem under Ore-type degree conditions, Pósa-type degree conditions, deficiency-type conditions and for balanced partite graphs.
Czech name
—
Czech description
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Project
<a href="/en/project/GA19-08740S" target="_blank" >GA19-08740S: Embedding, Packing and Limits in Graphs</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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