Autor: Fabrici, Igor - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On Vertices Enforcing a Hamiltonian Cycle
Autorzy:: Fabrici, Igor
Hexel, Erhard
Jendrol’, Stanislav
Powiązania:: https://bibliotekanauki.pl/articles/30146856.pdf
Data publikacji:: 2013-03-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: cycle
hamiltonian
1-hamiltonian
Opis:: A nonempty vertex set X ⊆ V (G) of a hamiltonian graph G is called an H-force set of G if every X-cycle of G (i.e. a cycle of G containing all vertices of X) is hamiltonian. The H-force number h(G) of a graph G is defined to be the smallest cardinality of an H-force set of G. In the paper the study of this parameter is introduced and its value or a lower bound for outerplanar graphs, planar graphs, k-connected graphs and prisms over graphs is determined.
Źródło:: Discussiones Mathematicae Graph Theory; 2013, 33, 1; 71-89
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: A note on vertex colorings of plane graphs
Autorzy:: Fabrici, Igor
Jendrol’, Stanislav
Soták, Roman
Powiązania:: https://bibliotekanauki.pl/articles/30148722.pdf
Data publikacji:: 2014-11-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: plane graph
vertex coloring
Opis:: Given an integer valued weighting of all elements of a 2-connected plane graph G with vertex set V, let c(v) denote the sum of the weight of v ∈ V and of the weights of all edges and all faces incident with v. This vertex coloring of G is proper provided that c(u) ≠ c(v) for any two adjacent vertices u and v of G. We show that for every 2-connected plane graph there is such a proper vertex coloring with weights in {1, 2, 3}. In a special case, the value 3 is improved to 2.
Źródło:: Discussiones Mathematicae Graph Theory; 2014, 34, 4; 849-855
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Colorings of Plane Graphs Without Long Monochromatic Facial Paths
Autorzy:: Czap, Július
Fabrici, Igor
Jendrol’, Stanislav
Powiązania:: https://bibliotekanauki.pl/articles/32222689.pdf
Data publikacji:: 2021-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: plane graph
facial path
vertex-coloring
Opis:: Let G be a plane graph. A facial path of G is a subpath of the boundary walk of a face of G. We prove that each plane graph admits a 3-coloring (a 2-coloring) such that every monochromatic facial path has at most 3 vertices (at most 4 vertices). These results are in a contrast with the results of Chartrand, Geller, Hedetniemi (1968) and Axenovich, Ueckerdt, Weiner (2017) which state that for any positive integer t there exists a 4-colorable (a 3-colorable) plane graph G_t such that in any its 3-coloring (2-coloring) there is a monochromatic path of length at least t. We also prove that every plane graph is 2-list-colorable in such a way that every monochromatic facial path has at most 4 vertices.
Źródło:: Discussiones Mathematicae Graph Theory; 2021, 41, 3; 801-808
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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