Results 11 to 20 of about 119,953 (318)
The game chromatic number of trees and forests [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 While the game chromatic number of a forest is known to be at most 4, no simple criteria are known for determining the game chromatic number of a forest. We first state necessary and sufficient conditions for forests with game chromatic number 2 and then
Charles Dunn +4 more
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Chromatic Vertex Folkman Numbers [PDF]
The Electronic Journal of Combinatorics, 2020 For graph $G$ and integers $a_1 \ge \cdots \ge a_r \ge 2$, we write $G \rightarrow (a_1 ,\cdots ,a_r)^v$ if and only if for every $r$-coloring of the vertex set $V(G)$ there exists a monochromatic $K_{a_i}$ in $G$ for some color $i \in \{1, \cdots, r\}$.
Xu, Xiaodong +2 more
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Distance graphs with maximum chromatic number [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let $D$ be a finite set of integers. The distance graph $G(D)$ has the set of integers as vertices and two vertices at distance $d ∈D$ are adjacent in $G(D)$.
Javier Barajas, Oriol Serra
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Dynamic Chromatic Number of Bipartite Graphs [PDF]
Scientific Annals of Computer Science, 2016 A dynamic coloring of a graph G is a proper vertex coloring such that for every vertex v Î V(G) of degree at least 2, the neighbors of v receive at least 2 colors.
S. Saqaeeyan, E. Mollaahamdi
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The -distance chromatic number of trees and cycles
AKCE International Journal of Graphs and Combinatorics, 2019 For any positive integer , a -distance coloring of a graph is a vertex coloring of in which no two vertices at distance less than or equal to receive the same color.
Niranjan P.K., Srinivasa Rao Kola
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Snarks with total chromatic number 5 [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Graph ...
Gunnar Brinkmann +2 more
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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
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Advances in Mathematics, 1999 From the article: We consider graphs \({\mathcal G}=(X,R)\) where the vertex set \(X\) is a standard Borel space (i.e., a complete separable metrizable space equipped with its \(\sigma\)-algebra of Borel sets), and the edge relation \(R\subseteq X^2\) is ``definable,'' i.e., Borel, analytic, coanalytic, etc.
Kechris, A. S. +2 more
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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
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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
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