기초과학연구원 이산수학그룹
We formulate a geometric version of the Erdős-Hajnal conjecture that applies to finite projective geometries rather than graphs. In fact, we give a natural extension of the 'multicoloured' version of …
The matroid intersection problem is a fundamental problem in combinatorial optimization. In this problem we are given two matroids and the goal is to find the largest common independent set …
We prove that for any circle graph $H$ with at least one edge and for any positive integer $k$, there exists an integer $t=t(k,H)$ so that every graph $G$ either …
Lehel's conjecture states that every 2-edge-colouring of the complete graph $K_n$ admits a partition of its vertices into two monochromatic cycles. This was proven for sufficiently large n by Luczak, …
We will discuss two symmetry breaking parameters: distinguishing number and fixing number. Despite being introduced independently, they share meaningful connections. In particular, we show that if a tree is 2-distinguishable …
We prove that for all positive integers $k$ and $d$, the class of $K_{1,d}$-free graphs not containing the $k$-ladder or the $k$-wheel as an induced minor has a bounded tree-independence …
Nowhere-zero flows of unsigned graphs were introduced by Tutte in 1954 as a dual problem to vertex-coloring of (unsigned) planar graphs. The definition of nowhere-zero flows on signed graphs naturally …
Given a $k$-uniform hypergraph $H$, the Ramsey number $R(H;q)$ is the smallest integer $N$ such that any $q$-coloring of the edges of the complete $k$-uniform hypergraph on $N$ vertices contains …
A graph $G$ is (list, DP) $k$-critical if the (list, DP) chromatic number is $k$ but for every proper subgraph $G'$ of $G$, the (list, DP) chromatic number of $G'$ …
Robertson and Seymour introduced branch-width as a connectivity invariant of graphs in their proof of the Wagner conjecture. Decompositions based on this invariant provide a natural framework for implementing dynamic-programming …