Temat: A2 - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: A note on periodicity of the 2-distance operator
Autorzy:: Zelinka, Bohdan
Powiązania:: https://bibliotekanauki.pl/articles/743805.pdf
Data publikacji:: 2000
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: 2-distance operator
complement of a graph
Opis:: The paper solves one problem by E. Prisner concerning the 2-distance operator T₂. This is an operator on the class $C_f$ of all finite undirected graphs. If G is a graph from $C_f$, then T₂(G) is the graph with the same vertex set as G in which two vertices are adjacent if and only if their distance in G is 2. E. Prisner asks whether the periodicity ≥ 3 is possible for T₂. In this paper an affirmative answer is given. A result concerning the periodicity 2 is added.
Źródło:: Discussiones Mathematicae Graph Theory; 2000, 20, 2; 267-269
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: A Degree Condition Implying Ore-Type Condition for Even [2, b]-Factors in Graphs
Autorzy:: Tsuchiya, Shoichi
Yashima, Takamasa
Powiązania:: https://bibliotekanauki.pl/articles/31341635.pdf
Data publikacji:: 2017-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: [ a, b ]-factor
even factor
2-edge-connected
minimum degree
Opis:: For a graph $G$ and even integers $ b \ge a \ge 2 $, a spanning subgraph $F$ of $G$ such that $ a \le \text{deg}_F (x) \le b $ and $ \text{deg}_F (x) $ is even for all $ x \in V (F) $ is called an even $[a, b]$-factor of $G$. In this paper, we show that a 2-edge-connected graph $G$ of order $n$ has an even $[2, b]$-factor if $ \text{max} \{ \text{deg}_G (x) , \text{deg}_G (y) \} \ge \text{max} \{ \frac{2n}{2+b} , 3 \} $ for any nonadjacent vertices $x$ and $y$ of $G$. Moreover, we show that for $ b \ge 3a$ and $a > 2$, there exists an infinite family of 2-edge-connected graphs $G$ of order $n$ with $ \delta (G) \ge a$ such that $G$ satisfies the condition $ \text{deg}_G (x) + \text{deg}_G (y) > \frac{2an}{a+b} $ for any nonadjacent vertices $x$ and $y$ of $G$, but has no even $[a, b]$-factors. In particular, the infinite family of graphs gives a counterexample to the conjecture of Matsuda on the existence of an even $[a, b]$-factor.
Źródło:: Discussiones Mathematicae Graph Theory; 2017, 37, 3; 797-809
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Partitions of a graph into cycles containing a specified linear forest
Autorzy:: Matsubara, Ryota
Matsumura, Hajime
Powiązania:: https://bibliotekanauki.pl/articles/743517.pdf
Data publikacji:: 2008
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: partition of a graph
vertex-disjoint cycle
2-factor
linear forest
Opis:: In this note, we consider the partition of a graph into cycles containing a specified linear forest. Minimum degree and degree sum conditions are given, which are best possible.
Źródło:: Discussiones Mathematicae Graph Theory; 2008, 28, 1; 97-107
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Solutions of Some L(2, 1)-Coloring Related Open Problems
Autorzy:: Mandal, Nibedita
Panigrahi, Pratima
Powiązania:: https://bibliotekanauki.pl/articles/31341092.pdf
Data publikacji:: 2016-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: span of a graph
no-hole coloring
irreducible coloring
unicyclic graph
L(2 1)-coloring
Opis:: An L(2, 1)-coloring (or labeling) of a graph G is a vertex coloring f : V (G) → Z⁺ ∪ {0} such that |f(u) − f(v)| ≥ 2 for all edges uv of G, and |f(u)−f(v)| ≥ 1 if d(u, v) = 2, where d(u, v) is the distance between vertices u and v in G. The span of an L(2, 1)-coloring is the maximum color (or label) assigned by it. The span of a graph G is the smallest integer λ such that there exists an L(2, 1)-coloring of G with span λ. An L(2, 1)-coloring of a graph with span equal to the span of the graph is called a span coloring. For an L(2, 1)-coloring f of a graph G with span k, an integer h is a hole in f if h ∈ (0, k) and there is no vertex v in G such that f(v) = h. A no-hole coloring is an L(2, 1)-coloring with no hole in it. An L(2, 1)-coloring is irreducible if color of none of the vertices in the graph can be decreased to yield another L(2, 1)-coloring of the same graph. A graph G is inh-colorable if there exists an irreducible no-hole coloring of G. Most of the results obtained in this paper are answers to some problems asked by Laskar et al. [5]. These problems are mainly about relationship between the span and maximum no-hole span of a graph, lower inh-span and upper inh-span of a graph, and the maximum number of holes and minimum number of holes in a span coloring of a graph. We also give some sufficient conditions for a tree and an unicyclic graph to have inh-span Δ + 1.
Źródło:: Discussiones Mathematicae Graph Theory; 2016, 36, 2; 279-297
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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