Autor: Jendroľ, Stanislav - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: An inequality concerning edges of minor weight in convex 3-polytopes
Autorzy:: Fabrici, Igor
Jendrol', Stanislav
Powiązania:: https://bibliotekanauki.pl/articles/972043.pdf
Data publikacji:: 1996
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: planar graph
convex 3-polytope
normal map
Opis:: Let $e_{ij}$ be the number of edges in a convex 3-polytope joining the vertices of degree i with the vertices of degree j. We prove that for every convex 3-polytope there is $20e_{3,3} + 25e_{3,4} + 16e_{3,5} + 10e_{3,6} + 6[2/3]e_{3,7} + 5e_{3,8} + 2[1/2]e_{3,9} + 2e_{3,10} + 16[2/3]e_{4,4} + 11e_{4,5} + 5e_{4,6} + 1[2/3]e_{4,7} + 5[1/3]e_{5,5} + 2e_{5,6} ≥ 120$; moreover, each coefficient is the best possible. This result brings a final answer to the conjecture raised by B. Grünbaum in 1973.
Źródło:: Discussiones Mathematicae Graph Theory; 1996, 16, 1; 81-87
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

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: 3.

Tytuł:: Paths of low weight in planar graphs
Autorzy:: Fabrici, Igor
Harant, Jochen
Jendrol', Stanislav
Powiązania:: https://bibliotekanauki.pl/articles/743525.pdf
Data publikacji:: 2008
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: planar graphs
polytopal graphs
paths
weight of an edge
weight of a path
Opis:: The existence of paths of low degree sum of their vertices in planar graphs is investigated. The main results of the paper are:
1. Every 3-connected simple planar graph G that contains a k-path, a path on k vertices, also contains a k-path P such that for its weight (the sum of degrees of its vertices) in G it holds
$w_G(P): = ∑_{u∈ V(P)} deg_G(u) ≤ (3/2)k² + (k)$
2. Every plane triangulation T that contains a k-path also contains a k-path P such that for its weight in T it holds
$w_T(P): = ∑_{u∈ V(P)} deg_T(u) ≤ k² +13 k$
3. Let G be a 3-connected simple planar graph of circumference c(G). If c(G) ≥ σ| V(G)| for some constant σ > 0 then for any k, 1 ≤ k ≤ c(G), G contains a k-path P such that
$w_G(P) = ∑_{u∈ V(P)} deg_G(u) ≤ (3/σ + 3)k$.
Źródło:: Discussiones Mathematicae Graph Theory; 2008, 28, 1; 121-135
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

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: 5.

Tytuł:: On Longest Cycles in Essentially 4-Connected Planar Graphs
Autorzy:: Fabrici, Igor
Harant, Jochen
Jendroľ, Stanislav
Powiązania:: https://bibliotekanauki.pl/articles/31340878.pdf
Data publikacji:: 2016-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: planar graph
longest cycle
Opis:: A planar 3-connected graph $ G $ is essentially 4-connected if, for any 3-separator $ S $ of $ G $, one component of the graph obtained from $ G $ by removing $ S $ is a single vertex. Jackson and Wormald proved that an essentially 4-connected planar graph on n vertices contains a cycle $ C $ such that $ |V(C)| \ge \frac{2n+4}{5} $. For a cubic essentially 4-connected planar graph $G$, Grünbaum with Malkevitch, and Zhang showed that $G$ has a cycle on at least $ \frac{3}{4} n $ vertices. In the present paper the result of Jackson and Wormald is improved. Moreover, new lower bounds on the length of a longest cycle of $G$ are presented if $G$ is an essentially 4-connected planar graph of maximum degree 4 or $G$ is an essentially 4-connected maximal planar graph.
Źródło:: Discussiones Mathematicae Graph Theory; 2016, 36, 3; 565-575
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 6.

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

Informacja