相关论文: On the Grundy number of Cameron graphs

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, is adjacent to (i - 1) vertices colored with each color j, In this…

The Grundy number of a graph $G$ is the maximum number of colors used by the First-Fit coloring of $G$ and is denoted by $\Gamma(G)$. Similarly, the ${\rm b}$-chromatic number ${\rm{b}}(G)$ of $G$ expresses the worst case behavior of…

A coloring of a graph G = (V,E) is a partition {V1, V2, . . ., Vk} of V into independent sets or color classes. A vertex v Vi is a Grundy vertex if it is adjacent to at least one vertex in each color class Vj . A coloring is a Grundy…

The Grundy number of a graph is the minimum number of colors needed to properly color the graph using the first-fit greedy algorithm regardless of the initial vertex ordering. Computing the Grundy number of a graph is an NP-Hard problem.…

For any graph $G$, the Grundy (or First-Fit) chromatic number of $G$, denoted by $\Gamma(G)$ (also $\chi_{_{\sf FF}}(G)$), is defined as the maximum number of colors used by the First-Fit (greedy) coloring of the vertices of $G$.…

A coloring of a graph $G=(V,E)$ is a partition $\{V_1, V_2, \ldots, V_k\}$ of $V$ into independent sets or color classes. A vertex $v\in V_i$ is a Grundy vertex if it is adjacent to at least one vertex in each color class $V_j$ for every…

A Grundy k-coloring of a graph G, is a vertex k-coloring of G such that for each two colors i and j with i < j, every vertex of G colored by j has a neighbor with color i. The Grundy chromatic number (G), is the largest integer k for which…

The Grundy and the {\rm b}-chromatic number of graphs are two important chromatic parameters. The Grundy number of a graph $G$, denoted by $\Gamma(G)$ is the worst case behavior of greedy (First-Fit) coloring procedure for $G$ and the {\rm…

The Grundy number of a graph is the maximum number of colors used by the greedy coloring algorithm over all vertex orderings. In this paper, we study the computational complexity of GRUNDY COLORING, the problem of determining whether a…

The Grundy number of a graph is the maximum number of colours used by the "First-Fit" greedy colouring algorithm over all vertex orderings. Given a vertex ordering $\sigma= v_1,\dots,v_n$, the "First-Fit" greedy colouring algorithm colours…

The pseudo-Grundy index of a graph is the largest number of colors that can be assigned to its edges, such that for every pair of colors $i,j$, if $i < j$ then every edge colored with color $j$ is adjacent to at least one edge colored with…

A map $c:V(G)\rightarrow\{1,\dots,k\}$ of a graph $G$ is a packing $k$-coloring if every two different vertices of the same color $i\in \{1,\dots,k\}$ are at distance more than $i$. The packing chromatic number $\chi_{\rho}(G)$ of $G$ is…

A proper vertex colouring of a graph is \emph{nested} if the vertices of each of its colour classes can be ordered by inclusion of their open neighbourhoods. Through a relation to partially ordered sets, we show that the nested chromatic…

A b-coloring of a graph is a proper coloring such that each color class has at least one vertex which is adjacent to each other color class. The b-spectrum of $G$ is the set $S_{b}(G)$ of integers $k$ such that $G$ has a b-coloring with $k$…

The Grundy (or First-Fit) chromatic number of a graph $G=(V,E)$, denoted by $\Gamma(G)$ (or $\chi_{_{\sf FF}}(G)$), is the maximum number of colors used by a First-Fit (greedy) coloring of $G$. To determine $\Gamma(G)$ is NP-complete for…

Our work becomes integrated into the general problem of the stability of the network ad hoc. Some, works attacked this problem. Among these works, we find the modelling of the network ad hoc in the form of a graph. Thus the problem of…

The curling number of a graph G is defined as the number of times an element in the degree sequence of G appears the maximum. Graph colouring is an assignment of colours, labels or weights to the vertices or edges of a graph. A colouring…

For a given number of colors, $s$, the guessing number of a graph is the (base $s$) logarithm of the cardinality of the largest family of colorings of the vertex set of the graph such that the color of each vertex can be determined from the…

In this paper, we investigate the \textsc{Grundy Coloring} problem for graphs with a cluster modulator, a structure commonly found in dense graphs. The Grundy chromatic number, representing the maximum number of colors needed for the…

Several authors modelled networks ad hoc by oriented or disoriented graphs, whereby the problem of allowance (allocation) of the frequencies at the level of the network was transformed into coloring problem of nodes in the graph. Graph…