6 problems

Buchanan et al.'s conjecture. For such $k$,

Let $G$ be an Eulerian graph, let $\Delta(G)$ be its maximum degree, and let a path odd-cover (respectively, cycle odd-cover) be a collection of paths (respectively, cycles) whose…

For a graph $G$, let $b_2(G)$ denote its biclique partition number over the field of two elements, and let $K_n$ denote the complete graph on $n$ vertices. Let $k$ be a positive in…

Let $G$ be an $n$-vertex graph. A path odd-cover is a collection of paths in the complete graph on $V(G)$ whose symmetric difference of edge sets is $E(G)$, and $p_2(G)$ is the min…

Let $b_2(G)$ denote the minimum dimension of a binary vector space in which the vertices of a graph $G$ can be represented as an odd cover, and let $K_m$ be the complete graph on…

Let $b_2(G)$ denote the minimum dimension of a binary vector space in which the vertices of a graph $G$ can be represented as an odd cover, and let $K_m$ be the complete graph on…