On Barnette’s conjecture and the $$H^{+-}$$ H + - property

Florek, Jan

doi:10.1007/s10878-014-9797-y

Cited by 5 publications

(10 citation statements)

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“…From (7), it follows that every graph (G, g) ∈ S n , for n > 10, is also opequivalent to one of the above graphs (or to a mirror reflection of one of them, for n odd). Finally, by (8) and Lemma 3.2, every graph (G, g) ∈ S n , different than (H 7 , g), has a hamiltonian set which is (±)compatible with the orientation of c(G). Lemma 4.6.…”

Section: Hamiltonian Sets In Graphs Of Small Heightsmentioning

confidence: 95%

“…Observe that, for an even n, there exists exactly 8 2 +8 = 36 different graphs in S n . Similarly, for an odd n, there exists exactly 2 8 2 + 8 = 64 different graphs in S n . Hence, by the definition of ω, it is not difficult to check that every graph (G, g) ∈ S n , where 6 n 10, is op-equivalent to one of the following graphs (or to a mirror reflection of one of them, for n odd):…”

Section: Hamiltonian Sets In Graphs Of Small Heightsmentioning

confidence: 96%

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Hamiltonian cycles in some family of cubic 3-connected plane graphs

Florek¹

2018

Colloq. Math.

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Section: Hamiltonian Sets In Graphs Of Small Heightsmentioning

confidence: 95%

Section: Hamiltonian Sets In Graphs Of Small Heightsmentioning

confidence: 96%

Hamiltonian cycles in some family of cubic 3-connected plane graphs

Florek¹

2018

Colloq. Math.

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“…Lysenko, Makarowicz, Ko kin, Šklarevskij 2011). 7 Por. Svešnikov 1968;Górski 1996Górski , 2010Kempisty 1967Kempisty , 1978Florek, Taras 2003;Makarowicz 2008Makarowicz , 2009Makarowicz , 2010aMakarowicz , 2010bMakarowicz, Lysenko, Ko kin 2013. 8 Sulimirski 1964, 1968Makarowicz 2008Makarowicz , 20092010b, 311-317. cji fizyczno-geograficznej teren ów jest fragmentem Przedkarpacia, granicz cym od północy z Wy yn Podolsk , a pod wzgl dem regionalizacji etnograficznej le y on w Galicji 9 .…”

Section: Usytuowanie Cmentarzyska I Układ Przestrzenny Kurhanówunclassified

Kurhany z epoki brązu nad górnym Dniestrem – polsko-ukraińskie projekty badawcze

Makarowicz

Lysenko

Kočkin³

2013

10.14746/fpp

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dzynarodowych Przykarpackiego Narodowego Uniwersytetu im. V. Stefanika ul. Šev enki 57, 76000 Ivano-Frankivs'k, UkraineABSTRACT. This paper discuses the excavations in the cemetery of the Komarów culture of the Bronze Age in Bukivna upon the upper Dniester. They have been carried out by the Polish-Ukrainian archaeological expedition as a part of the project of the National Centre of Sciences, the aim of which has been to provide comprehensive bioarchaeological characteristic and socio-cultural interpretation of the cemetery. During the field walking over 50 barrows were documented, round or slightly oval in plan. They occurred in three main clusters, arranged in groups-lines, on the watershed between the Dniester and its little, nameless tributary.The article presents the results of the study of barrow 1, in which there were discovered six features and over 400 artefacts, including 38 vessels in several deposits, 262 flint implements, fragments of structural daub, and bronze items -a pin and pendant, as well as small, burned bones.Among the features two charred wooden structures seem special and one stone-and-wood (cenotaph). Bones were "scattered" mainly between wooden structures.A series of analyses and specialist expertises had been done: radiocarbon, paleopedological, geomorphological, paleobotanical, physico-chemical. The sum of probability distribution of calibrated radiocarbon dates suggests second quarter of the second millennium BC. These dates are consistent with the analysis of the stylistics of vessels and bronze artefacts, indicating the early and classic stages of development of the Komarów culture.

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“…Denote by B i the set of all big vertices in V i , i = 1, 2, 3. Let P G denote the family of all paths P of length at least 2 in G, with big ends and small inner vertices such that either P is an induced path in G, or the ends a, b of P are adjacent and P + ab is an induced cycle in G. Florek [4] proved the following lemma:…”

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confidence: 99%

“…Hence, by the Stein theorem, {e * ∈ E(G * ) : e ∈ E(S, T )} is the set of edges of a Hamilton cycle in the dual graph G * . Moreover, Florek [4]…”

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confidence: 99%

Graphs with multi-$4$-cycles and the Barnette's conjecture

Florek

2020

Preprint

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Let H denote the family of all graphs with multi-4-cycles and suppose that G ∈ H. Then, G is a bipartite graph with a vertex bipartition {V α , V β }. We prove that for every vertex v ∈ V β and for every 2-colouringLet now G be a simple even plane triangulation with a vertex 3-partitionthen, for any edge chosen on a face coloured 3 and of size at least 6 in G * , there exists a Hamilton cycle of G * which avoids this edge. Moreover, if every component of H is 2-connected, then there exists a Hamilton cycle of G * such that for every face coloured 3 it avoids every second edge of this face or it avoids at most two edges of this face.

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On Barnette’s conjecture and the $$H^{+-}$$ H + - property

Cited by 5 publications

References 6 publications

Hamiltonian cycles in some family of cubic 3-connected plane graphs

Hamiltonian cycles in some family of cubic 3-connected plane graphs

Kurhany z epoki brązu nad górnym Dniestrem – polsko-ukraińskie projekty badawcze

Graphs with multi-$4$-cycles and the Barnette's conjecture

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