Related papers: BDD-Based Algorithm for SCC Decomposition of Edge-…
We study weighted edge coloring of graphs, where we are given an undirected edge-weighted general multi-graph $G := (V, E)$ with weights $w : E \rightarrow [0, 1]$. The goal is to find a proper weighted coloring of the edges with as few…
We present results on partitioning the vertices of $2$-edge-colored graphs into monochromatic paths and cycles. We prove asymptotically the two-color case of a conjecture of S\'ark\"ozy: the vertex set of every $2$-edge-colored graph can be…
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.…
Given an undirected graph $G=(V,E)$ with a set of vertices $V$ and a set of edges $E$, a graph coloring problem involves finding a partition of the vertices into different independent sets. In this paper we present a new framework that…
We introduce a dense counterpart of graph degeneracy, which extends the recently-proposed invariant symmetric difference. We say that a graph has sd-degeneracy (for symmetric-difference degeneracy) at most $d$ if it admits an elimination…
We propose a novel method to cluster gene networks. Based on a dissimilarity built using correlation structures, we consider networks that connect all the genes based on the strength of their dissimilarity. The large number of genes require…
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…
A well-studied coloring problem is to assign colors to the edges of a graph $G$ so that, for every pair of vertices, all edges of at least one shortest path between them receive different colors. The minimum number of colors necessary in…
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…
Network decomposition is a central concept in the study of distributed graph algorithms. We present the first polylogarithmic-round deterministic distributed algorithm with small messages that constructs a strong-diameter network…
Type-4 clones refer to a pair of code snippets with similar semantics but written in different syntax, which challenges the existing code clone detection techniques. Previous studies, however, highly rely on syntactic structures and textual…
A graph is a powerful concept for representation of relations between pairs of entities. Data with underlying graph structure can be found across many disciplines and there is a natural desire for understanding such data better. Deep…
The GRAPH MOTIF problem asks whether a given multiset of colors appears on a connected subgraph of a vertex-colored graph. The fastest known parameterized algorithm for this problem is based on a reduction to the $k$-Multilinear Detection…
Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…
The goal of the thesis is to leverage fast graph algorithms and modern algorithmic techniques for problems in model checking and synthesis on graphs, MDPs, and game graphs. The results include symbolic algorithms, a well-known class of…
We call a (not necessarily properly) edge-colored graph edge-color-avoiding connected if after the removal of edges of any single color, the graph remains connected. For vertex-colored graphs, similar definitions of color-avoiding…
Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and…
There is an extensive literature on dynamic algorithms for a large number of graph theoretic problems, particularly for all varieties of shortest path problems. Germane to this paper are a number fully dynamic algorithms that are known for…
Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…
Given a non-decreasing sequence S = (s 1,s 2,. .. ,s k) of positive integers, an S-packing edge-coloring of a graph G is a partition of the edge set of G into k subsets {X 1 ,X 2,. .. ,X k } such that for each 1 $\le$ i $\le$ k, the…