Total $\{k\}$-domination in caterpillars: Structural properties and exact results

Mariana Escalante, Paola Tolomei, María Inés Lopez Pujato

The total $\{k\}$-domination problem ($T\{k\}DP$) seeks a minimum-weight function such that the sum of weights in every open neighborhood is at least $k$. While this problem is kno…