2020/09/11 by Joseph S. Alameda, Alameda, Joseph S., Juergen Kritschgau +3 · 2 citations
Computer Science · Engineering · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #VLSI and FPGA Design Techniques
paper · pdf · doi:10.48550/arxiv.2009.07073
openalex publication_date 2020/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Vertex leaky forcing was recently introduced as a new variation of zero forcing in order to show how vertex leaks can disrupt the zero forcing process in a graph. An edge leak is an edge that is not allowed to be forced across during the zero forcing process. The ℓ-edge-leaky forcing number of a graph is the size of a smallest zero forcing set that can force the graph blue despite ℓ edge leaks. This paper contains an analysis of the effect of edge leaks on the zero forcing process instead of vertex leaks. Furthermore, specified ℓ-leaky forcing is introduced. The main result is that ℓ-leaky forcing, ℓ-edge-leaky forcing, and specified ℓ-leaky forcing are equivalent. Furthermore, all of these different kinds of leaks can be mixed so that vertex leaks, edge leaks, and specified leaks are used. This mixed ℓ-leaky forcing number is also the same as the (vertex) ℓ-leaky forcing number.