기초과학연구원 이산수학그룹
Amazon drivers hit the road every day, each taking a Prime van in a traveling salesman problem tour through 150 or more customer stops. But even a whisper of the TSP strikes fear in the heart of the computing world. A Washington Post article reported it would take "1,000 years to compute the most efficient …
We prove a conjecture of Bonamy, Bousquet, Pilipczuk, Rzążewski, Thomassé, and Walczak, that for every graph
Let
Bollobás proved that for every
The positive discrepancy of a graph
Delta-matroids are a generalization of matroids with connections to many parts of graph theory and combinatorics (such as matching theory and the structure of topological graph embeddings). Formally, a delta-matroid is a pair
We say that two functors Λ and Γ between thin categories of relational structures are adjoint if for all structures A and B, we have that Λ(A) maps homomorphically to B if and only if A maps homomorphically to Γ(B). If this is the case Λ is called the left adjoint to Γ and Γ …
A family
In 2017, Aharoni proposed the following generalization of the Caccetta-Häggkvist conjecture for digraphs. If G is a simple n-vertex edge-colored graph with n color classes of size at least r, then G contains a rainbow cycle of length at most ⌈n/r⌉. In this talk, we prove that Aharoni's conjecture holds up to an additive constant. …
A cross-cap drawing of a graph G is a drawing on the sphere with g distinct points, called cross-caps, such that the drawing is an embedding except at the cross-caps, where edges cross properly. A cross-cap drawing of a graph G with g cross-caps can be used to represent an embedding of G on a …