Bounded vertex coloring of trees

Edge-coloring Vertex-weightings of Graphs

Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $n$. A $k$-vertex weightings of a graph $G$ is a mapping $w: V(G) to {1, ldots, k}$. A $k$-vertex weighting induces an edge labeling $f_w: E(G) to N$ such that $f_w(uv)=w(u)+w(v)$. Such a labeling is called an {it edge-coloring k-vertex weightings} if $f_{w}(e)not= f_{w}(echr(chr(chr('39')39chr('39'))39chr(chr('39')39chr('39'...

Deterministic Distributed (Delta + o(Delta))-Edge-Coloring, and Vertex-Coloring of Graphs with Bounded Diversity

In the distributed message-passing setting a communication network is represented by a graph whose vertices represent processors that perform local computations and communicate over the edges of the graph. In the distributed edge-coloring problem the processors are required to assign colors to edges, such that all edges incident on the same vertex are assigned distinct colors. The previouslykno...

Symmetry Breaking in Trees and Planar Graphs by Vertex Coloring

An undirected graph G is said to be d-distinguishable if there is a d-coloring of its vertex set V (G) such that no nontrivial automorphism of G preserves the coloring. The distinguishing number of a graph G is the minimum d for which it is d-distinguishable. In this paper we design efficient algorithms for computing the distinguishing numbers of trees and planar graphs.

Vertex Equitable Labelings of Transformed Trees

Vertex-Coloring with Defects

Defective coloring is a variant of the traditional vertex-coloring in which adjacent vertices are allowed to have the same color, as long as the induced monochromatic components have a certain structure. Due to its important applications, as for example in the bipartisation of graphs, this type of coloring has been extensively studied, mainly with respect to the size, degree, diameter, and acyc...