20.500.12556/DiRROS-23662 Spreading in claw-free cubic graphs Let $p\in\mathbb{N}$ and $q\in\mathbb{N}\cup\{\infty\}$. We study a dynamic coloring of the vertices of a graph $G$ that starts with an initial subset $S$ of blue vertices, with all remaining vertices colored white. If a white vertex $v$ has at least $p$ blue neighbors and at least one of these blue neighbors of $v$ has at most $q$ white neighbors, then by the spreading color change rule the vertex $v$ is recolored blue. The initial set $S$ of blue vertices is a $(p,q)$-spreading set for $G$ if by repeatedly applying the spreading color change rule all the vertices of $G$ are eventually colored blue. The $(p,q)$-spreading set is a generalization of the well-studied concepts of $k$-forcing and $r$-percolating sets in graphs. For $q\ge2$, a $(1,q)$-spreading set is exactly a $q$-forcing set, and the $(1,1)$-spreading set is a $1$-forcing set (also called a zero forcing set), while for $q=\infty$, a $(p,\infty)$-spreading set is exactly a $p$-percolating set. The $(p,q)$-spreading number, $\sigma_{(p,q)}(G)$, of $G$ is the minimum cardinality of a $(p,q)$-spreading set. In this paper, we study $(p,q)$-spreading in claw-free cubic graphs. While the zero-forcing number of claw-free cubic graphs was studied earlier, for each pair of values $p$ and $q$ that are not both $1$ we either determine the $(p,q)$-spreading number of a claw-free cubic graph $G$ or show that $\sigma_{(p,q)}(G)$ attains one of two possible values. bootstrap percolation zero forcing set k-forcing set spreading ojačano pronicanje množica ničelne prisile množica k-prisile razširjanje true false true Angleški jezik Slovenski jezik Neznano 2025-09-23 09:40:01 2025-09-23 09:40:02 2025-10-24 03:54:46 0000-00-00 00:00:00 2025 0 0 str. 581-600 no. 5 Vol. 45 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-01-01 519.17 1232-9274 10.7494/OpMath.2025.45.5.581 249948163 opuscula_math_4527.pdf opuscula_math_4527.pdf 1 9A39310687CBE79264838F22D35677BA afb052eb0e07bea2f9171a022cd34c175160cc4591647cadd401d363a8485701 31477307-9851-11f0-9bb7-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=35031 https://www.opuscula.agh.edu.pl/om-vol45iss5art1 1 899f4bf9-9850-11f0-9bb7-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=35030 Inštitut za matematiko, fiziko in mehaniko 0 0 0