This paper investigates the properties of tree-width and related graph width parameters for
nSuperHyperGraphs, a broader generalization of hypergraphs. By exploring concepts such …

A vertex colouring of a graph $ G $ is" nonrepetitive" if $ G $ contains no path for which the
first half of the path is assigned the same sequence of colours as the second half. Thue's …

The purpose of this survey is to bring some order into the growing literature on a type of
graphs which emerged in the past couple of decades under a wealth of names and in …

An edge-coloring of a graph G is acyclic if it is a proper edge-coloring of G and every cycle
contains at least three colors. We prove that every graph with maximum degree Δ has an …

A queue layout of a graph consists of a total order of the vertices, and a partition of the edges
into queues, such that no two edges in the same queue are nested. The minimum number of …

We provide a “how-to” guide to the use and application of the Discharging Method. Our aim
is not to exhaustively survey results proved by this technique, but rather to demystify the …

Graph coloring is one of the best known, popular and extensively researched subject in the
field of graph theory, having many applications and conjectures, which are still open and …

A vertex coloring φ of a graph G is p-centered if for every connected subgraph H of G either
φ uses more than p colors on H or there is a color that appears exactly once on H Centered …

Classes with bounded expansion, which generalise classes that exclude a topological
minor, have recently been introduced by Nešetřil and Ossona de Mendez. These classes …

Given a graph G with maximum degree Δ≥ 3, we prove that the acyclic edge chromatic
number a′(G) of G is such that a′(G)≤⌈ 9.62 (Δ− 1)⌉. Moreover we prove that: a′(G)≤⌈ …