Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 3

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Generalized chromatic numbers and additive hereditary properties of graphs

100%
Broere I., Dorfling S., Jonck E.
Discussiones Mathematicae Graph Theory
|
2002
|
tom 22
|
nr 2
259-270
EN
An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. Let 𝓟 and 𝓠 be additive hereditary properties of graphs. The generalized chromatic number $χ_{𝓠}(𝓟)$ is defined as follows: $χ_{𝓠}(𝓟) = n$ iff 𝓟 ⊆ 𝓠 ⁿ but $𝓟 ⊊ 𝓠^{n-1}$. We investigate the generalized chromatic numbers of the well-known properties of graphs 𝓘ₖ, 𝓞ₖ, 𝓦ₖ, 𝓢ₖ and 𝓓ₖ.
2
Content available remote

The Degree-Diameter Problem for Outerplanar Graphs

100%
Dankelmann P., Jonck E., Vetrík T.
Discussiones Mathematicae Graph Theory
|
2017
|
tom 37
|
nr 3
823-834
EN
For positive integers Δ and D we define nΔ,D to be the largest number of vertices in an outerplanar graph of given maximum degree Δ and diameter D. We prove that [...] nΔ,D=ΔD2+O (ΔD2−1) $n_{\Delta ,D} = \Delta ^{{D \over 2}} + O\left( {\Delta ^{{D \over 2} - 1} } \right)$ is even, and [...] nΔ,D=3ΔD−12+O (ΔD−12−1) $n_{\Delta ,D} = 3\Delta ^{{{D - 1} \over 2}} + O\left( {\Delta ^{{{D - 1} \over 2} - 1} } \right)$ if D is odd. We then extend our result to maximal outerplanar graphs by showing that the maximum number of vertices in a maximal outerplanar graph of maximum degree Δ and diameter D asymptotically equals nΔ,D.
3
Content available remote

A lower bound for the packing chromatic number of the Cartesian product of cycles

100%
Jacobs Y., Jonck E., Joubert E.
Open Mathematics
|
2013
|
tom 11
|
nr 7
1344-1357
EN
Let G = (V, E) be a simple graph of order n and i be an integer with i ≥ 1. The set X i ⊆ V(G) is called an i-packing if each two distinct vertices in X i are more than i apart. A packing colouring of G is a partition X = {X 1, X 2, …, X k} of V(G) such that each colour class X i is an i-packing. The minimum order k of a packing colouring is called the packing chromatic number of G, denoted by χρ(G). In this paper we show, using a theoretical proof, that if q = 4t, for some integer t ≥ 3, then 9 ≤ χρ(C 4 □ C q). We will also show that if t is a multiple of four, then χρ(C 4 □ C q) = 9.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.