All Questions

Consider a $k$ regular graph of $n$ vertices, where $3 \leq k \leq (n-1)$. Is there any upper or lower bound, in the worst case, known for either the tree-width or the clique width of each $k$ regular ...

The definition of block is Block of $G$ is a maximal subgraph $G'$ of $G$ with no cut vertex of $G'$ itself. Of course, there can exist many blocks in $G$. In particular, isolated vertices, edges in ...

I want to prove that ‘If the girth of a $2k$-regular graph $G$ is larger than the diameter of a $k$-edge tree $T$, then $G$ is covered by edge-disjoint copies of $T$.’ I tried several ways to solve ...