‎Let $G$ be a graph and $chi^{prime}_{aa}(G)$ denotes the minimum number of colors required for an‎ ‎acyclic edge coloring of $G$ in which no two adjacent vertices are incident to edges colored with the same set of colors‎. ...

Recently, E. M'{a}v{c}ajov'{a} and M. v{S}koviera proved that every bidirected Eulerian graph which admits a nowhere zero flow, admits a nowhere zero $4$-flow. This result shows the validity of Bouchet's nowhere zero ...

We define $[k]={1‎, ‎2‎, ‎3,ldots,k}$ to be a (totally ordered) {em alphabet} on $k$ letters‎. ‎A {em word} $w$ of length $n$ on the alphabet $[k]$ is an element of $[k]^n$‎. ‎A word can be represented by a bargraph which ...