기초과학연구원 이산수학그룹
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A k-coloring of a graph is an assignment of k colors to its vertices such that no two adjacent adjacent vertices receive the same color. The Coloring Problem is the problem of determining the smallest k such that the graph admits a k-coloring. Given a set L of graphs, a graph G is L-free if … |
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Directed graphs prove to be very hard to tame in contrast to undirected graphs. In particular, they are not well-quasi-ordered by any known relevant inclusion relation, and are lacking fruitful structure theorems. This motivates the search for structurally rich subclasses of directed graphs that are well behaved. Eulerian directed graphs are a particularly prominent example, … |
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Two related papers will be discussed: 1. In 1966, Erdős, Goodman, and Pósa showed that if $G$ is an $n$-vertex graph, then at most $\lfloor n^2/4 \rfloor$ cliques of $G$ are needed to cover the edges of $G$, and the bound is best possible as witnessed by the balanced complete bipartite graph. This was generalized … |
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A backedge graph of a tournament $T$ with respect to a total ordering $\prec$ of the vertices of $T$ is a graph on $V(T)$ where $uv$ is an edge if and only if $uv \in A(T)$ and $v \prec u$. In 2023, Aboulker, Aubian, Charbit and Lopes introduced the clique number of tournaments based on … |
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