In the study of temporal graphs, only paths respecting the flow of time are relevant. In this context, many concepts of walk disjointness have been proposed over the years and the validity of Menger's Theorem, as well as the complexity of related ...

• A novel type of temporal paths disjointness.
• Introduction of related parameters: maximum number of snapshot disjoint paths and minimum size of a snapshot cut.
• Tight classification of related problems when parameterized by solution ...

For a fixed positive integer d ≥ 2, a distance-d independent set (DdIS) of a graph is a vertex-subset whose distance between any two members is at least d. Imagine that there is a token placed on each member of a DdIS. Two DdISs are adjacent ...

The Square Colouring of a graph G refers to colouring of vertices of a graph such that any two distinct vertices which are at distance at most two receive different colours. In this paper, we initiate the study of a related colouring problem ...

In an undirected graph G = ( V , E ), we say that ( A , B ) is a pair of perfectly matched sets if A and B are disjoint subsets of V and every vertex in A (resp. B) has exactly one neighbor in B (resp. A). The size of a pair of perfectly matched ...

As usual λ ( G ) denotes the edge-connectivity of the graph G. It was shown in [2] that every graph G contains a spanning ( λ ( G ) + 1 )-partite subgraph H such that λ ( H ) = λ ( G ) and one can find such a spanning subgraph in ...

We present a procedure for efficiently sampling colors in the CONGEST model. It allows nodes whose number of colors exceeds their number of neighbors by a constant fraction to sample up to Θ ( log ⁡ n ) semi-random colors unused by ...

• Ultrafast distributed coloring is possible even with bandwidth constraints.
• ...

In this paper, we consider a matching in a bipartite graph where each vertex has a preference over the edges incident to it. Especially, we consider the case where a preference of a vertex is defined based on comparisons of any two ...

• We consider a bipartite graph with pairwise preferences.
• We consider a Pareto ...

The page-number of a directed acyclic graph (a DAG, for short) is the minimum k for which the DAG has a topological order and a k-coloring of its edges such that no two edges of the same color cross, i.e., have alternating endpoints along the ...

A properly colored walk, is a walk where every two consecutive edges have different colors, including the first and last edges in the case when the walk is closed. Properly colored walks have shown to be an effective way to model certain real ...

Coloring unit-disk graphs efficiently is an important problem in the global and distributed setting, with applications in radio channel assignment problems when the communication relies on omni-directional antennas of the same power. ...

• We present a new distributed algorithm for coloring unit-disk graphs, when nodes are aware of their coordinates.

The total angular resolution of a straight-line drawing is the minimum angle between two edges of the drawing. It combines two properties contributing to the readability of a drawing: the angular resolution, which is the minimum angle ...

We introduce a variant of the graph coloring problem, which we denote as Budgeted Coloring Problem (BCP). Given a graph G, an integer c and an ordered list of integers ( b 1 , b 2 , … , b c ), BCP asks whether there exists a proper ...

The diamond is the graph obtained by removing an edge from the complete graph on 4 vertices. A graph is (P 6, diamond)-free if it contains no induced subgraph isomorphic to a six-vertex path or a diamond. In this paper we show that the ...

• We obtain an improved bound on the chromatic number of (P 6, diamond)-free graphs.

The vertex-arboricity of a graph G, denoted by v a ( G ), is the minimum number of subsets in which V ( G ) can be partitioned so that each subset induces a forest. It is known that v a ( G ) ≤ 3 for every planar graph G and v a ( G ) ≤...

A proper k-edge-colouring ϕ of a graph G is an assignment of colours from { 1 , … , k } to the edges of G such that no two adjacent edges receive the same colour. If, additionally, ϕ guarantees that no two adjacent vertices of G are ...

Let G be a graph, and ℓ : E ( G ) → { 1 , … , k } be a k-labelling of G, i.e., an assignment of labels from { 1 , … , k } to the edges of G. We say that ℓ is irregular if no two distinct vertices of G are incident to the same sum of ...

A digraph D is singly connected if for all ordered pairs of vertices u , v ∈ V ( D ), there is at most one path in D from u to v. In this paper, we study the Singly Connected Vertex Deletion (SCVD) problem: Given an n-vertex digraph D ...

A vertex coloring of a graph G = ( V , E ) is called an exact square coloring of G if any two vertices at distance exactly 2 receive different colors. The minimum number of colors required by an exact square coloring is called the ...

For a fixed integer, the k -Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for an integer k, such that no two adjacent vertices are coloured alike. A graph G is H-free if ...

A (finite or infinite) graph is called constructible if it may be obtained recursively from the one-point graph by repeatedly adding dominated vertices. In the finite case, the constructible graphs are precisely the cop-win graphs, but ...