기초과학연구원 이산수학그룹
We show that for pairs (Q,R) and (S,T) of disjoint subsets of vertices of a graph G, if G is sufficiently large, then there exists a vertex v in V(G)−(Q∪R∪S∪T) such …
We call an induced cycle of length at least four a hole. The parity of a hole is the parity of its length. Forbidding holes of certain types in a graph …
The Weighted $\mathcal F$-Vertex Deletion for a class $\mathcal F$ of graphs asks, given a weighted graph $G$, for a minimum weight vertex set $S$ such that $G-S\in\mathcal F$. The …
Given a graph $G$, a dominating set of $G$ is a set $S$ of vertices such that each vertex not in $S$ has a neighbor in $S$. The domination number of $G$, …
For a rational number $q= s/r$, we consider the two 2x2 matrices $A=\begin{pmatrix}1&0\\1&1\end{pmatrix}$ and $B_q=\begin{pmatrix}1&q\\0&1\end{pmatrix}$. It is a long-standing conjecture (traced at least back to Rimhak Ree) that A and …