Perfect graphs for domination games
Csilla Bujt\'as, Vesna Ir\v{s}i\v{c}, Sandi Klav\v{z}ar

TL;DR
This paper characterizes perfect graphs related to domination game parameters, providing polynomial recognition algorithms and identifying minimal imperfect graphs, especially within triangle-free graphs and cographs.
Contribution
It introduces recursive characterizations for b3_g- and b3_tg-perfect graphs, and identifies minimal imperfect graphs, advancing understanding of domination game perfection.
Findings
Polynomial recognition algorithm for b3_g-perfect graphs.
All minimally b3_g-imperfect graphs have domination number 2.
b3_tg-perfect graphs are exactly b1;b4;2P_3-free cographs.
Abstract
Let and be the game domination number and the total game domination number of a graph , respectively. Then is -perfect (resp. -perfect), if every induced subgraph of satisfies (resp. ). A recursive characterization of -perfect graphs is derived. The characterization yields a polynomial recognition algorithm for -perfect graphs. It is proved that every minimally -imperfect graph has domination number . All minimally -imperfect triangle-free graphs are determined. It is also proved that -perfect graphs are precisely -free cographs.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
