Temat: plane - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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: 2.

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

Skocz do pozycji: 3.

Tytuł:: Unique-Maximum Coloring Of Plane Graphs
Autorzy:: Fabrici, Igor
Göring, Frank
Powiązania:: https://bibliotekanauki.pl/articles/31341171.pdf
Data publikacji:: 2016-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: plane graph
weak-parity coloring
unique-maximum coloring
Opis:: A unique-maximum k-coloring with respect to faces of a plane graph G is a coloring with colors 1, . . ., k so that, for each face of G, the maximum color occurs exactly once on the vertices of α. We prove that any plane graph is unique-maximum 3-colorable and has a proper unique-maximum coloring with 6 colors.
Źródło:: Discussiones Mathematicae Graph Theory; 2016, 36, 1; 95-102
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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