Further results on the Hunters and Rabbit game through monotonicity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F25%3A00385536" target="_blank" >RIV/68407700:21240/25:00385536 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.ic.2025.105302" target="_blank" >https://doi.org/10.1016/j.ic.2025.105302</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ic.2025.105302" target="_blank" >10.1016/j.ic.2025.105302</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Further results on the Hunters and Rabbit game through monotonicity

Popis výsledku v původním jazyce

The Hunters and Rabbit game is played on a graph G where the Hunter player shoots at k vertices in every round while the Rabbit player occupies an unknown vertex and, if not shot, must move to a neighbouring vertex. The Rabbit player wins if and only if it is not shot indefinitely. The hunter number h(G ) of a graph G is the minimum k such that the Hunter player has a winning strategy. We propose a notion of monotonicity, embodied in the monotone hunter number mh(G ), for this game imposing that a vertex that has already been shot ``must not host the rabbit anymore''. We show that p w (G ) <= mh(G ) <= p w (G ) + 1 for any graph G with pathwidth p w (G ), implying that computing, or even approximating, mh(G ) is NP-hard. Then, we show that mh(G ) can be computed in polynomial time in split graphs, interval graphs, cographs and trees. These results go through structural characterisations which relate the monotone hunter number with the pathwidth. In all these cases, we either specify the hunter number or show that there may be an arbitrary gap between h and mh, i.e., that monotonicity does not help. In particular, for every k >= 3, we construct a tree T with h( T ) = 2 and mh( T ) = k. We conclude by proving that computing h (resp., mh) is FPT parameterised by the vertex cover number.

Název v anglickém jazyce

Further results on the Hunters and Rabbit game through monotonicity

Popis výsledku anglicky

The Hunters and Rabbit game is played on a graph G where the Hunter player shoots at k vertices in every round while the Rabbit player occupies an unknown vertex and, if not shot, must move to a neighbouring vertex. The Rabbit player wins if and only if it is not shot indefinitely. The hunter number h(G ) of a graph G is the minimum k such that the Hunter player has a winning strategy. We propose a notion of monotonicity, embodied in the monotone hunter number mh(G ), for this game imposing that a vertex that has already been shot ``must not host the rabbit anymore''. We show that p w (G ) <= mh(G ) <= p w (G ) + 1 for any graph G with pathwidth p w (G ), implying that computing, or even approximating, mh(G ) is NP-hard. Then, we show that mh(G ) can be computed in polynomial time in split graphs, interval graphs, cographs and trees. These results go through structural characterisations which relate the monotone hunter number with the pathwidth. In all these cases, we either specify the hunter number or show that there may be an arbitrary gap between h and mh, i.e., that monotonicity does not help. In particular, for every k >= 3, we construct a tree T with h( T ) = 2 and mh( T ) = k. We conclude by proving that computing h (resp., mh) is FPT parameterised by the vertex cover number.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Information and Computation

ISSN

0890-5401

e-ISSN

1090-2651

Svazek periodika

305

Číslo periodika v rámci svazku

June

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

31

Strana od-do

—

Kód UT WoS článku

001510321200001

EID výsledku v databázi Scopus

2-s2.0-105004359923