相关论文: b-continuity and Partial Grundy Coloring of graphs…

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…

A vertex coloring $\phi$ of a graph $G$ is $p$-centered if for every connected subgraph $H$ of $G$ either $\phi$ uses more than $p$ colors on $H$ or there is a color that appears exactly once on $H$. Centered colorings form one of the…

We show that every (sub)cubic n-vertex graph with sufficiently large girth has fractional chromatic number at most 2.2978 which implies that it contains an independent set of size at least 0.4352n. Our bound on the independence number is…

A star edge coloring of a graph is a proper edge coloring with no $2$-colored path or cycle of length four. The star chromatic index $\chi'_{st}(G)$ of $G$ is the minimum number $t$ for which $G$ has a star edge coloring with $t$ colors. We…

The \textit{square} of a graph $G$, denoted by $G^2$, is obtained from $G$ by adding an edge to connect every pair of vertices with a common neighbor in $G$. In this paper we prove that for every planar graph $G$ with maximum degree at most…

Coloring a graph $G$ consists in finding an assignment of colors $c: V(G)\to\{1,\ldots,p\}$ such that any pair of adjacent vertices receives different colors. The minimum integer $p$ such that a coloring exists is called the chromatic…

An $acyclic$ edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycle s. The \emph{acyclic chromatic index} of a graph is the minimum number k such that there is an acyclic e dge coloring using k colors…

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…

In a bounded max-coloring of a vertex/edge weighted graph, each color class is of cardinality at most $b$ and of weight equal to the weight of the heaviest vertex/edge in this class. The bounded max-vertex/edge-coloring problems ask for…

A packing $k$-coloring of a graph $G$ is a partition of $V(G)$ into sets $V_1,\ldots,V_k$ such that for each $1\leq i\leq k$ the distance between any two distinct $x,y\in V_i$ is at least $i+1$. The packing chromatic number, $\chi_p(G)$, of…

A vertex coloring of a graph $G$ is called a 2-distance coloring if any two vertices at a distance at most $2$ from each other receive different colors. Suppose that $G$ is a planar graph with girth $5$ and maximum degree $\Delta$. We prove…

For a graph G and an integer t we let mcc_t(G) be the smallest m such that there exists a coloring of the vertices of G by t colors with no monochromatic connected subgraph having more than m vertices. Let F be any nontrivial minor-closed…

A proper conflict-free coloring of a graph is a proper vertex coloring wherein each non-isolated vertex's open neighborhood contains at least one color appearing exactly once. For a non-negative integer $k$, a graph $G$ is said to be proper…

We denote by $\chi$ g (G) the game chromatic number of a graph G, which is the smallest number of colors Alice needs to win the coloring game on G. We know from Montassier et al. [M. Montassier, P. Ossona de Mendez, A. Raspaud and X. Zhu,…

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…

An $(a:b)$-coloring of a graph $G$ is a function $f$ which maps the vertices of $G$ into $b$-element subsets of some set of size $a$ in such a way that $f(u)$ is disjoint from $f(v)$ for every two adjacent vertices $u$ and $v$ in $G$. The…

We show that every planar graph $G$ has a 2-fold 9-coloring. In particular, this implies that $G$ has fractional chromatic number at most $\frac92$. This is the first proof (independent of the 4 Color Theorem) that there exists a constant…

Graph coloring problems are a central topic of study in the theory of algorithms. We study the problem of partially coloring partially colorable graphs. For $\alpha \leq 1$ and $k \in \mathbb{Z}^+$, we say that a graph $G=(V,E)$ is…

A graph is $(d_1, \ldots, d_k)$-colorable if its vertex set can be partitioned into $k$ nonempty subsets so that the subgraph induced by the $i$th part has maximum degree at most $d_i$ for each $i\in\{1, \ldots, k\}$. It is known that for…

An $r$-hued coloring of a simple graph $G$ is a proper coloring of its vertices such that every vertex $v$ is adjacent to at least $\min\{r, \deg(v)\}$ differently colored vertices. The minimum number of colors needed for an $r$-hued…