Geodesic
Span of a Graph: Keeping the Safety Distance
Discrete mathematics & theoretical computer science, Tome 25 (2023-2024) no. 1.

Voir la notice de l'article provenant de la source Episciences

Inspired by Lelek's idea from [Disjoint mappings and the span of spaces, Fund. Math. 55 (1964), 199 -- 214], we introduce the novel notion of the span of graphs. Using this, we solve the problem of determining the \emph{maximal safety distance} two players can keep at all times while traversing a graph. Moreover, their moves must be made with respect to certain move rules. For this purpose, we introduce different variants of a span of a given connected graph. All the variants model the maximum safety distance kept by two players in a graph traversal, where the players may only move with accordance to a specific set of rules, and their goal: visit either all vertices, or all edges. For each variant, we show that the solution can be obtained by considering only connected subgraphs of a graph product and the projections to the factors. We characterise graphs in which it is impossible to keep a positive safety distance at all moments in time. Finally, we present a polynomial time algorithm that determines the chosen span variant of a given graph.
DOI : 10.46298/dmtcs.9859
Classification : 05C12, 05C57, 05C76, 91A43 
@article{DMTCS_2023_25_1_a5,
     author = {Bani\v{c}, Iztok and Taranenko, Andrej},
     title = {Span of a {Graph:} {Keeping} the {Safety} {Distance}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2023-2024},
     doi = {10.46298/dmtcs.9859},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.9859/}
}
TY  - JOUR
AU  - Banič, Iztok
AU  - Taranenko, Andrej
TI  - Span of a Graph: Keeping the Safety Distance
JO  - Discrete mathematics & theoretical computer science
PY  - 2023-2024
VL  - 25
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.9859/
DO  - 10.46298/dmtcs.9859
LA  - en
ID  - DMTCS_2023_25_1_a5
ER  - 
%0 Journal Article
%A Banič, Iztok
%A Taranenko, Andrej
%T Span of a Graph: Keeping the Safety Distance
%J Discrete mathematics & theoretical computer science
%D 2023-2024
%V 25
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.9859/
%R 10.46298/dmtcs.9859
%G en
%F DMTCS_2023_25_1_a5
Banič, Iztok; Taranenko, Andrej. Span of a Graph: Keeping the Safety Distance. Discrete mathematics & theoretical computer science, Tome 25 (2023-2024) no. 1. doi : 10.46298/dmtcs.9859. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.9859/

Cité par Sources :