Effect of predomination and vertex removal on the game total domination\n number of a graph

2018/02/10 by Vesna Iršič, Iršič, Vesna · 1 citation
Computer Science · #05C57 #05C69 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1802.03637

openalex publication_date 2018/02/10 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

The game total domination number, \γ_g^t, was introduced by\nHenning et al. in 2015. In this paper we study the effect of vertex\npredomination on the game total domination number. We prove that\n\γ_g^t(G|v) \≥ \γ_g^t(G) - 2 holds for all vertices v\nof a graph G and present infinite families attaining the equality. To achieve\nthis, some new variations of the total domination game are introduced. The\neffect of vertex removal is also studied. We show that \γ_g^t(G)\n\≤ \γ_g^t(G-v) + 4 and \γ_g^t'(G) \≤\n\γ_g^t'(G-v) + 4.\n

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