Related papers: Rainbow Greedy Matching Algorithms
A rainbow matching in an edge-coloured graph is a matching such that its edges have distinct colours. We show that every properly edge-coloured graph $G$ with $|G| \ge (9\delta(G) -5)/2$ has a rainbow matching of size $\delta(G)$, improving…
An edge (vertex) coloured graph is rainbow-connected if there is a rainbow path between any two vertices, i.e. a path all of whose edges (internal vertices) carry distinct colours. Rainbow edge (vertex) connectivity of a graph $G$ is the…
State of the art maximum clique algorithms use a greedy graph colouring as a bound. We show that greedy graph colouring can be misleading, which has implications for parallel branch and bound.
A {\it rainbow matching} in an edge-colored graph is a matching in which all the edges have distinct colors. Wang asked if there is a function f(\delta) such that a properly edge-colored graph G with minimum degree \delta and order at least…
Given an edge-colored graph, the Maximum Rainbow Matching problem asks for a maximum-cardinality matching of the graph that contains at most one edge from each color. We provide the following complexity dichotomy for this problem based on…
A rainbow matching in an edge-colored graph is a matching in which no two edges have the same color. The color degree of a vertex v is the number of different colors on edges incident to v. Kritschgau [Electron. J. Combin. 27(2020)] studied…
Given a vertex-colored graph, we say a path is a rainbow vertex path if all its internal vertices have distinct colors. The graph is rainbow vertex-connected if there is a rainbow vertex path between every pair of its vertices. In the…
An edge-colored graph $G$ is said to be rainbow connected if between each pair of vertices there exists a path which uses each color at most once. The rainbow connection number, denoted by $rc(G)$, is the minimum number of colors needed to…
Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…
We study the greedy-based online algorithm for edge-weighted matching with (one-sided) vertex arrivals in bipartite graphs, and edge arrivals in general graphs. This algorithm was first studied more than a decade ago by Korula and P\'al for…
We study a version of online edge coloring, where the goal is to color as many edges as possible using only a given number, $k$, of available colors. All of our results are with regard to competitive analysis. Previous attempts to identify…
An edge-colored multigraph $G$ is rainbow connected if every pair of vertices is joined by at least one rainbow path, i.e., a path where no two edges are of the same color. In the context of multilayered networks we introduce the notion of…
Given a large social or information network, how can we partition the vertices into sets (i.e., colors) such that no two vertices linked by an edge are in the same set while minimizing the number of sets used. Despite the obvious practical…
A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices.…
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…
Given a graph on $n$ vertices and an assignment of colours to the edges, a rainbow Hamilton cycle is a cycle of length $n$ visiting each vertex once and with pairwise different colours on the edges. Similarly (for even $n$) a rainbow…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
A properly edge-colored graph is a graph with a coloring of its edges such that no vertex is incident to two or more edges of the same color. A subgraph is called rainbow if all its edges have different colors. The problem of finding…
We define and study greedy matchings in vertex-ordered bipartite graphs. It is shown that each vertex-ordered bipartite graph has a unique greedy matching. The proof uses (a weak form of) Newman's lemma. The vertex ordering is called a…
Let $G$ be an edge-colored graph. We use $e(G)$ and $c(G)$ to denote the number of edges and colors in $G$, respectively. A subgraph $H$ is called rainbow if $c(H)=e(H)$. Li et al. (European J. Combin., 36 (2014), 453-459) proved that every…