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Wyświetlanie 1-15 z 27
Tytuł:
Vertex-Distinguishing IE-Total Colorings of Complete Bipartite Graphs Km,N(m < n)
Autorzy:
Chen, Xiang’en
Gao, Yuping
Yao, Bing
Powiązania:
https://bibliotekanauki.pl/articles/30146641.pdf
Data publikacji:
2013-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
complete bipartite graphs
IE-total coloring
vertex-distinguishing IE-total coloring
vertex-distinguishing IE-total chromatic number
Opis:
Let G be a simple graph. An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. Let C(u) be the set of colors of vertex u and edges incident to u under f. For an IE-total coloring f of G using k colors, if C(u) ≠ C(v) for any two different vertices u and v of G, then f is called a k-vertex-distinguishing IE-total-coloring of G, or a k-VDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χievt(G), and is called vertex-distinguishing IE-total chromatic number or the VDIET chromatic number of G for short. VDIET colorings of complete bipartite graphs Km,n(m < n) are discussed in this paper. Particularly, the VDIET chromatic numbers of Km,n(1 ≤ m ≤ 7, m < n) as well as complete graphs Kn are obtained.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 2; 289-306
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Vertex-distinguishing edge-colorings of linear forests
Autorzy:
Cichacz, Sylwia
Przybyło, Jakub
Powiązania:
https://bibliotekanauki.pl/articles/744522.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
irregular edge-coloring
vertex-distinguishing edge-coloring
point-distinguishing chromatic index
Opis:
In the PhD thesis by Burris (Memphis (1993)), a conjecture was made concerning the number of colors c(G) required to edge-color a simple graph G so that no two distinct vertices are incident to the same multiset of colors. We find the exact value of c(G) - the irregular coloring number, and hence verify the conjecture when G is a vertex-disjoint union of paths. We also investigate the point-distinguishing chromatic index, χ₀(G), where sets, instead of multisets, are required to be distinct, and determine its value for the same family of graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2010, 30, 1; 95-103
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Vertex rainbow colorings of graphs
Autorzy:
Fujie-Okamoto, Futaba
Kolasinski, Kyle
Lin, Jianwei
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/743667.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
rainbow path
vertex rainbow coloring
vertex rainbow connection number
Opis:
In a properly vertex-colored graph G, a path P is a rainbow path if no two vertices of P have the same color, except possibly the two end-vertices of P. If every two vertices of G are connected by a rainbow path, then G is vertex rainbow-connected. A proper vertex coloring of a connected graph G that results in a vertex rainbow-connected graph is a vertex rainbow coloring of G. The minimum number of colors needed in a vertex rainbow coloring of G is the vertex rainbow connection number vrc(G) of G. Thus if G is a connected graph of order n ≥ 2, then 2 ≤ vrc(G) ≤ n. We present characterizations of all connected graphs G of order n for which vrc(G) ∈ {2,n-1,n} and study the relationship between vrc(G) and the chromatic number χ(G) of G. For a connected graph G of order n and size m, the number m-n+1 is the cycle rank of G. Vertex rainbow connection numbers are determined for all connected graphs of cycle rank 0 or 1 and these numbers are investigated for connected graphs of cycle rank 2.
Źródło:
Discussiones Mathematicae Graph Theory; 2012, 32, 1; 63-80
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Three edge-coloring conjectures
Autorzy:
Schelp, Richard
Powiązania:
https://bibliotekanauki.pl/articles/743559.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge-coloring
Ramsey number
vertex-distinguishing edge-coloring
strong chromatic index
balanced edge-coloring
local coloring
mean coloring
Opis:
The focus of this article is on three of the author's open conjectures. The article itself surveys results relating to the conjectures and shows where the conjectures are known to hold.
Źródło:
Discussiones Mathematicae Graph Theory; 2002, 22, 1; 173-182
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Vertex-Rainbow Index of A Graph
Autorzy:
Mao, Yaping
Powiązania:
https://bibliotekanauki.pl/articles/31340818.pdf
Data publikacji:
2016-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
vertex-coloring
connectivity
vertex-rainbow S-tree
vertex- rainbow index
Nordhaus-Gaddum type
Opis:
The k-rainbow index rxk(G) of a connected graph G was introduced by Chartrand, Okamoto and Zhang in 2010. As a natural counterpart of the k-rainbow index, we introduce the concept of k-vertex-rainbow index rvxk(G) in this paper. In this paper, sharp upper and lower bounds of rvxk(G) are given for a connected graph G of order n, that is, 0 ≤ rvxk(G) ≤ n − 2. We obtain Nordhaus-Gaddum results for 3-vertex-rainbow index of a graph G of order n, and show that rvx3(G) + rvx3(Ḡ) = 4 for n = 4 and 2 ≤ rvx3(G) + rvx3(Ḡ) ≤ n − 1 for n ≥ 5. Let t(n, k, ℓ) denote the minimal size of a connected graph G of order n with rvxk(G) ≤ ℓ, where 2 ≤ ℓ ≤ n − 2 and 2 ≤ k ≤ n. Upper and lower bounds on t(n, k, ℓ) are also obtained.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 3; 669-681
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Star Coloring of Subcubic Graphs
Autorzy:
Karthick, T.
Subramanian, C.R.
Powiązania:
https://bibliotekanauki.pl/articles/30146582.pdf
Data publikacji:
2013-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
vertex coloring
star coloring
subcubic graphs
Opis:
A star coloring of an undirected graph G is a coloring of the vertices of G such that (i) no two adjacent vertices receive the same color, and (ii) no path on 4 vertices is bi-colored. The star chromatic number of G, χs(G), is the minimum number of colors needed to star color G. In this paper, we show that if a graph G is either non-regular subcubic or cubic with girth at least 6, then χs(G) ≤ 6, and the bound can be realized in linear time.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 2; 373-385
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Parity vertex colorings of binomial trees
Autorzy:
Gregor, Petr
Škrekovski, Riste
Powiązania:
https://bibliotekanauki.pl/articles/743737.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
binomial tree
parity coloring
vertex ranking
Opis:
We show for every k ≥ 1 that the binomial tree of order 3k has a vertex-coloring with 2k+1 colors such that every path contains some color odd number of times. This disproves a conjecture from [1] asserting that for every tree T the minimal number of colors in a such coloring of T is at least the vertex ranking number of T minus one.
Źródło:
Discussiones Mathematicae Graph Theory; 2012, 32, 1; 177-180
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On twin edge colorings of graphs
Autorzy:
Andrews, Eric
Helenius, Laars
Johnston, Daniel
VerWys, Jonathon
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/30148690.pdf
Data publikacji:
2014-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge coloring
vertex coloring
factorization
Opis:
A twin edge $k$-coloring of a graph $G$ is a proper edge coloring of $G$ with the elements of $\mathbb{Z}_k$ so that the induced vertex coloring in which the color of a vertex $v$ in $G$ is the sum (in $\mathbb{Z}_k$) of the colors of the edges incident with $v$ is a proper vertex coloring. The minimum $k$ for which $G$ has a twin edge $k$-coloring is called the twin chromatic index of $G$. Among the results presented are formulas for the twin chromatic index of each complete graph and each complete bipartite graph
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 3; 613-627
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Rainbow Vertex-Connection
Autorzy:
Li, Xueliang
Shi, Yongtang
Powiązania:
https://bibliotekanauki.pl/articles/30146636.pdf
Data publikacji:
2013-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
rainbow vertex-connection
vertex coloring
minimum degree
2-step dominating set
Opis:
A vertex-colored graph is rainbow vertex-connected if any two vertices are connected by a path whose internal vertices have distinct colors. The rainbow vertex-connection of a connected graph $G$, denoted by $rvc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow vertex-connected. It was proved that if $G$ is a graph of order $n$ with minimum degree $ \delta $, then $ rvc(G) < 11n//\delta$. In this paper, we show that $rvc(G) \le 3n//(δ+1)+5$ for $ \delta \ge \sqrt{n-1} -1 $ and $ n \le 290 $, while $ rvc(G) \le 4n//(δ + 1) + 5 $ for $ 16 \le \delta \le \sqrt{n-1}-2 $ and $ rvc(G) \le 4n//(\delta + 1) + C(\delta) $ for $6 \le \delta \le 15$, where $ C(\delta) = e^\frac{ 3 \log (\delta^3 + 2 \delta^2 +3)-3(\log 3 - 1)}{\delta - 3} - 2$. We also prove that $ rvc(G) \le 3n//4 − 2 $ for $ \delta = 3$, $ rvc(G) \le 3n//5 − 8//5$ for $\delta = 4$ and $rvc(G) \le n//2 − 2$ for $\delta = 5$. Moreover, an example constructed by Caro et al. shows that when $ \delta \ge \sqrt{n-1} - 1 $ and $ \delta = 3, 4, 5 $, our bounds are seen to be tight up to additive constants.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 2; 307-313
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On multiset colorings of graphs
Autorzy:
Okamoto, Futaba
Salehi, Ebrahim
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/744555.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
vertex coloring
multiset coloring
neighbor-distinguishing coloring
Opis:
A vertex coloring of a graph G is a multiset coloring if the multisets of colors of the neighbors of every two adjacent vertices are different. The minimum k for which G has a multiset k-coloring is the multiset chromatic number χₘ(G) of G. For every graph G, χₘ(G) is bounded above by its chromatic number χ(G). The multiset chromatic numbers of regular graphs are investigated. It is shown that for every pair k, r of integers with 2 ≤ k ≤ r - 1, there exists an r-regular graph with multiset chromatic number k. It is also shown that for every positive integer N, there is an r-regular graph G such that χ(G) - χₘ(G) = N. In particular, it is shown that χₘ(Kₙ × K₂) is asymptotically √n. In fact, $χₘ(Kₙ × K₂) = χₘ(cor(K_{n+1}))$. The corona cor(G) of a graph G is the graph obtained from G by adding, for each vertex v in G, a new vertex v' and the edge vv'. It is shown that χₘ(cor(G)) ≤ χₘ(G) for every nontrivial connected graph G. The multiset chromatic numbers of the corona of all complete graphs are determined. On Multiset Colorings of Graphs From this, it follows that for every positive integer N, there exists a graph G such that χₘ(G) - χₘ(cor(G)) ≥ N. The result obtained on the multiset chromatic number of the corona of complete graphs is then extended to the corona of all regular complete multipartite graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2010, 30, 1; 137-153
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Efficient coloring of chordless graphs
Autorzy:
Janczewski, R.
Małafiejski, M.
Powiązania:
https://bibliotekanauki.pl/articles/375900.pdf
Data publikacji:
2009
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
vertex coloring
chordless graphs
chromatic number
Opis:
We are given a simple graph G = (V,E). Any edge e ∈ E is a chord in a path P ⊆ G (cycle C ⊆ G) iff a graph obtained by joining e to path P (cycle C) has exactly two vertices of degree 3. A class of graphs without any chord in paths (cycles) we call pathchordless (cycle-chordless). We will prove that recognizing and coloring of these graphs can be done in O(n2) and O(n) time, respectively. Our study was motivated by a wide range of applications of the graph coloring problem in coding theory, time tabling and scheduling, frequency assignment, register allocation and many other areas.
Źródło:
Decision Making in Manufacturing and Services; 2009, 3, 1-2; 5-14
1896-8325
2300-7087
Pojawia się w:
Decision Making in Manufacturing and Services
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
New models and algorithms for RNA pseudoknot order assignment
Autorzy:
Zok, Tomasz
Badura, Jan
Swat, Sylwester
Figurski, Kacper
Popenda, Mariusz
Antczak, Maciej
Powiązania:
https://bibliotekanauki.pl/articles/911230.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
RNA pseudoknot order
conflict graph
vertex coloring
maximum independent set
integer programming
kolorowanie grafu
zbiór niezależny
programowanie całkowitoliczbowe
Opis:
The pseudoknot is a specific motif of the RNA structure that highly influences the overall shape and stability of a molecule. It occurs when nucleotides of two disjoint single-stranded fragments of the same chain, separated by a helical fragment, interact with each other and form base pairs. Pseudoknots are characterized by great topological diversity, and their systematic description is still a challenge. In our previous work, we have introduced the pseudoknot order: a new coefficient representing the topological complexity of the pseudoknotted RNA structure. It is defined as the minimum number of base pair set decompositions, aimed to obtain the unknotted RNA structure. We have suggested how it can be useful in the interpretation and understanding of a hierarchy of RNA folding. However, it is not trivial to unambiguously identify pseudoknots and determine their orders in an RNA structure. Therefore, since the introduction of this coefficient, we have worked on the method to reliably assign pseudoknot orders in correspondence to the mechanisms that control the biological process leading to their formation in the molecule. Here, we introduce a novel graph coloring-based model for the problem of pseudoknot order assignment. We show a specialized heuristic operating on the proposed model and an alternative integer programming algorithm. The performance of both approaches is compared with that of state-of-the-art algorithms which so far have been most efficient in solving the problem in question. We summarize the results of computational experiments that evaluate our new methods in terms of classification quality on a representative data set originating from the non-redundant RNA 3D structure repository.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 2; 315-324
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Kaleidoscopic Colorings of Graphs
Autorzy:
Chartrand, Gary
English, Sean
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/31341692.pdf
Data publikacji:
2017-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge coloring
vertex coloring
kaleidoscopic coloring
kaleidoscope
Opis:
For an $r$-regular graph $G$, let $ c : E(G) \rightarrow [k] = {1, 2, . . ., k}$, $ k \ge 3 $, be an edge coloring of $G$, where every vertex of $G$ is incident with at least one edge of each color. For a vertex $v$ of $G$, the multiset-color $ c_m(v)$ of $v$ is defined as the ordered $k$-tuple $ (a_1, a_2, . . ., a_k) $ or $ a_1a_2…a_k$, where $a_i$ $(1 \le i \le k)$ is the number of edges in $G$ colored $i$ that are incident with $v$. The edge coloring $c$ is called $k$-kaleidoscopic if $ c_m(u) \ne c_m(v)$ for every two distinct vertices $u$ and $v$ of $G$. A regular graph $G$ is called a $k$-kaleidoscope if $G$ has a $k$-kaleidoscopic coloring. It is shown that for each integer $k \ge 3 $, the complete graph $ K_{k+3}$ is a $k$-kaleidoscope and the complete graph $ K_n $ is a 3-kaleidoscope for each integer $ n \ge 6 $. The largest order of an $r$-regular 3-kaleidoscope is \( \binom{r-1}{2} \). It is shown that for each integer $ r \ge 5 $ such that \( r \not\equiv 3 (\text{mod } 4) \), there exists an $r$-regular 3-kaleidoscope of order \( \binom{r-1}{2} \).
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 3; 711-727
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Grundy number of graphs
Autorzy:
Effantin, Brice
Kheddouci, Hamamache
Powiązania:
https://bibliotekanauki.pl/articles/743619.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Grundy coloring
vertex coloring
cartesian product
graph product
Opis:
The Grundy number of a graph G is the maximum number k of colors used to color the vertices of G such that the coloring is proper and every vertex x colored with color i, 1 ≤ i ≤ k, is adjacent to (i-1) vertices colored with each color j, 1 ≤ j ≤ i -1. In this paper we give bounds for the Grundy number of some graphs and cartesian products of graphs. In particular, we determine an exact value of this parameter for n-dimensional meshes and some n-dimensional toroidal meshes. Finally, we present an algorithm to generate all graphs for a given Grundy number.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 1; 5-18
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized Hypergraph Coloring
Autorzy:
Schweser, Thomas
Powiązania:
https://bibliotekanauki.pl/articles/32083810.pdf
Data publikacji:
2021-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hypergraph decomposition
vertex partition
degeneracy
coloring of hypergraphs
hypergraph properties
Opis:
A smooth hypergraph property \(\mathcal{P}\) is a class of hypergraphs that is hereditary and non-trivial, i.e., closed under induced subhypergraphs and it contains a non-empty hypergraph but not all hypergraphs. In this paper we examine \(\mathcal{P}\)-colorings of hypergraphs with smooth hypergraph properties \(\mathcal{P}\). A \(\mathcal{P}\)-coloring of a hypergraph $H$ with color set $C$ is a function $\varphi : V(H) → C$ such that \(H\big[\varphi^{−1}(c)\big]\) belongs to \(\mathcal{P}\) for all $c ∈ C$. Let $L : V (H) → 2^C$ be a so called list-assignment of the hypergraph $H$. Then, a (\(\mathcal{P}, L\))-coloring of $H$ is a \(\mathcal{P}\)-coloring $\varphi$ of $H$ such that $\varphi(v) ∈ L(v)$ for all $v ∈ V (H)$. The aim of this paper is a characterization of (\(\mathcal{P}, L\))-critical hypergraphs. Those are hypergraphs $H$ such that $H − v$ is (\(\mathcal{P}, L\))-colorable for all $v ∈ V (H)$ but $H$ itself is not. Our main theorem is a Gallai-type result for critical hypergraphs, which implies a Brooks-type result for (\(\mathcal{P}, L\))-colorable hypergraphs. In the last section, we prove a Gallai-type bound for the degree sum of (\(\mathcal{P}, L\))-critical locally simple hypergraphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 1; 103-121
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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