Revisiting the Hamiltonian theme in the square of a block: the Case of DT-graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F18%3A43950238" target="_blank" >RIV/49777513:23520/18:43950238 - isvavai.cz</a>
Result on the web
<a href="http://intlpress.com/site/pub/pages/journals/items/joc/content/vols/0009/0001/a007/index.html" target="_blank" >http://intlpress.com/site/pub/pages/journals/items/joc/content/vols/0009/0001/a007/index.html</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4310/JOC.2018.v9.n1.a7" target="_blank" >10.4310/JOC.2018.v9.n1.a7</a>

Result language
angličtina
Original language name
Revisiting the Hamiltonian theme in the square of a block: the Case of DT-graphs
Original language description
The square of a graph G, denoted G^2, is the graph obtained from G by joining by an edge any two nonadjacent vertices which have a common neighbor. A graph G is said to have F_k property if for any set of k distinct vertices {x_1,x_2,...,x_k} in G, there is a hamiltonian path from x_1 to x_2 in G^2 containig k-2 distinct edges of G of the form x_i z_i, i=3,...,k. In [7], it was proved that every 2-connected graph has the F_3 property. In the first part of this work, we extend this result by proving that every 2-connected DT-graph has the F_4 property (Theorem 2) and will show in the second part that this generalization holds for arbitrary 2-connected graphs, and that there exist 2-connected graphs which do not have the F_k property for any natural number k>=5. Altogether, this answers the second problem raised in [4] in the affirmative.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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