Ringi Kim (김린기), The strong clique number of graphs with forbidden cycles
Room B232 IBS (기초과학연구원)The strong clique number of a graph
The strong clique number of a graph
A dibond in a directed graph is a bond (i.e. a minimal non-empty cut) for which all of its edges are directed to a common side of the cut. A famous theorem of Lucchesi and Younger states that in every finite digraph the least size of an edge set meeting every dicut equals the maximum …
In 1964, Erdős, Hajnal and Moon introduced a saturation version of Turán's classical theorem in extremal graph theory. In particular, they determined the minimum number of edges in a
For a vertex v of a graph G, the local complementation at v is an operation to obtain a new graph denoted by G*v from G such that two distinct vertices x, y are adjacent in G*v if and only if both x, y are neighbors of v and x, y are non-adjacent, or at least one …
Given a graph
KSIAM 2020 Spring Conference will be held at IBS from May 8, 2020 to May 9, 2020. Organized by Korean Society for Industrial and Applied Mathematics. Organizing Committee Myungjoo Kang (Seoul National University) (chair) Ahn, Jaemyung (KAIST) Kwon, Hee-Dae (Inha University) Lee, Eun Jung (Yonsei University) Jang, Bongsoo (UNIST) Jung, Miyoun (Hankuk University of Foreign …
Inspired by a width invariant defined on permutations by Guillemot and Marx , we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs,
Vatshelle (2012) introduced a width parameter called mim-width. It is based on the following cut function : for a vertex partition (A,B) of a graph, the complexity of this partition is computed by the size of a maximum induced matching of the bipartite subgraph induced by edges between A and B. This parameter naturally extends …
The famous Erdős-Rademacher problem asks for the smallest number of r-cliques in a graph with the given number of vertices and edges. Despite decades of active attempts, the asymptotic value of this extremal function for all r was determined only recently, by Reiher . Here we describe the asymptotic structure of all almost extremal graphs. …
The cut-rank of a set X of vertices in a graph G is defined as the rank of the X×(V(G)∖X) matrix over the binary field whose (i,j)-entry is 1 if the vertex i in X is adjacent to the vertex j in V(G)∖X and 0 otherwise. We introduce the graph parameter called the average cut-rank …