All Questions

Question: find the size of a maximal subset $A$ of $[n]=\{1,\cdots,n\}$ satisfying that for any distinct elements $x,y\in A$, $x+y$ is not a perfect square. Consider a graph with $n$ vertices: $x$ and ...

By a classical theorem of Nash-Williams, the edges of every connected $n$-vertex planar graph can be covered by three trees $T_1,T_2$ and $T_3$. Does anyone know of any results from an article or a ...

Consider simple connected undirected graphs $G = (V, E)$ equipped with a function $w\colon E\rightarrow \{x\in \mathbb{R}\colon x\geq 0\}$. Define a function $d_{G,w}\colon V\times V\rightarrow\...

let $A=\lbrace a_1,\,\dots,\,a_k\rbrace $ and $B=\lbrace b_1,\,\dots,\,b_{2k}\rbrace,\ A\cap B=\emptyset$ be be a partition of a graph's vertex set $V$, i.e. $V\,=\,A\cup B$. Question: has $G:=\...