Results 31 to 40 of about 9,612,020 (345)
Generalisasi Bilangan Kromatik Pada Beberapa Kelas Graf Korona
Jurnal Derivat, 2022 For example is a chromatic number with the smallest integer so that the graph has a true vertex coloring with k color. Chromatic number is still an interesting study which is still being studied for its development through graph coloring.
Riduan Yusuf +3 more
doaj +1 more source
On the dominated chromatic number of certain graphs [PDF]
Transactions on Combinatorics, 2020 Let $G$ be a simple graph. The dominated coloring of $G$ is a proper coloring of $G$ such that each color class is dominated by at least one vertex.
Saeid Alikhani, Mohammad Reza Piri
doaj +1 more source
Packing chromatic number versus chromatic and clique number [PDF]
Aequationes mathematicae, 2017 The packing chromatic number $ _ (G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set of $G$ can be partitioned into sets $V_i$, $i\in [k]$, where each $V_i$ is an $i$-packing. In this paper, we investigate for a given triple $(a,b,c)$ of positive integers whether there exists a graph $G$ such that $ (G) = a$, $ (G) = b$, and $
Boštjan Brešar +3 more
openaire +3 more sources
Discussiones Mathematicae Graph Theory, 2001 Let \(\tau(G)\) denote the number of vertices in a longest path of a graph \(G\). The \(n\)th detour number \(\chi_n(G)\) of a graph \(G\) is the minimum number of colours required to colour the vertices of \(G\) such that no path with more than \(n\) vertices is monocoloured. It is shown that the path partition conjecture, formulated by P. Mihók (see \
Frick, Marietjie, Bullock, Frank
openaire +1 more source
The Distinguishing Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2006 In this paper we define and study the distinguishing chromatic number, $\chi_D(G)$, of a graph $G$, building on the work of Albertson and Collins who studied the distinguishing number. We find $\chi_D(G)$ for various families of graphs and characterize those graphs with $\chi_D(G)$ $ = |V(G)|$, and those trees with the maximum chromatic distingushing ...
Collins, Karen L., Trenk, Ann N.
openaire +2 more sources
On the local distinguishing chromatic number
AKCE International Journal of Graphs and Combinatorics, 2019 The distinguishing number of graphs is generalized in two directions by Cheng and Cowen (local distinguishing number) and Collins and Trenk (Distinguishing chromatic number). In this paper, we define and study the local distinguishing chromatic number of
Omid Khormali
doaj +2 more sources
Snarks with total chromatic number 5 [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Graph ...
Gunnar Brinkmann +2 more
doaj +1 more source
Graphs with tiny vector chromatic numbers and huge chromatic numbers [PDF]
The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings., 2003 Summary: \textit{D. Karger, R. Motwani} and \textit{M. Sudan} [J. ACM 45, 246--265 (1998; Zbl 0904.68116)] introduced the notion of a vector coloring of a graph. In particular, they showed that every \(k\)-colorable graph is also vector \(k\)-colorable, and that for constant \(k\), graphs that are vector \(k\)-colorable can be colored by roughly ...
Feige, Uriel +2 more
openaire +2 more sources
Non-concentration of the chromatic number of a random graph [PDF]
, 2019 We show that the chromatic number of $G_{n, \frac 12}$ is not concentrated on fewer than $n^{\frac 14 - \varepsilon}$ consecutive values. This addresses a longstanding question raised by Erdős and several other authors.
Annika Heckel
semanticscholar +1 more source
Chromatic-Choosability of Hypergraphs with High Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2019 It was conjectured by Ohba and confirmed by Noel, Reed and Wu that, for any graph $G$, if $|V(G)|\le 2\chi(G)+1$ then $G$ is chromatic-choosable; i.e., it satisfies $\chi_l(G)=\chi(G)$. This indicates that the graphs with high chromatic number are chromatic-choosable. We observe that this is also the case for uniform hypergraphs and further propose a
Wang, Wei, Qian, Jianguo
openaire +3 more sources