2021
Computational Complexity of Covering Multigraphs with Semi-Edges: Small Cases
BOK, Jan, Jiří FIALA, Petr HLINĚNÝ, Nikola JEDLIČKOVÁ, Jan KRATOCHVÍL et. al.Základní údaje
Originální název
Computational Complexity of Covering Multigraphs with Semi-Edges: Small Cases
Autoři
BOK, Jan (203 Česká republika), Jiří FIALA (203 Česká republika), Petr HLINĚNÝ (203 Česká republika, garant, domácí), Nikola JEDLIČKOVÁ (203 Česká republika) a Jan KRATOCHVÍL (203 Česká republika)
Vydání
Dagstuhl, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021), od s. "21:1"-"21:15", 15 s. 2021
Nakladatel
Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik
Další údaje
Jazyk
angličtina
Typ výsledku
Stať ve sborníku
Obor
10201 Computer sciences, information science, bioinformatics
Stát vydavatele
Německo
Utajení
není předmětem státního či obchodního tajemství
Forma vydání
elektronická verze "online"
Odkazy
Kód RIV
RIV/00216224:14330/21:00119288
Organizační jednotka
Fakulta informatiky
ISBN
978-3-95977-201-3
ISSN
Klíčová slova anglicky
graph cover; covering projection; semiedges; multigraphs; complexity
Štítky
Příznaky
Mezinárodní význam, Recenzováno
Změněno: 19. 4. 2022 10:10, prof. RNDr. Petr Hliněný, Ph.D.
Anotace
V originále
We initiate the study of computational complexity of graph coverings, aka locally bijective graph homomorphisms, for graphs with semi-edges. The notion of graph covering is a discretization of coverings between surfaces or topological spaces, a notion well known and deeply studied in classical topology. Graph covers have found applications in discrete mathematics for constructing highly symmetric graphs, and in computer science in the theory of local computations. In 1991, Abello et al. asked for a classification of the computational complexity of deciding if an input graph covers a fixed target graph, in the ordinary setting (of graphs with only edges). Although many general results are known, the full classification is still open. In spite of that, we propose to study the more general case of covering graphs composed of normal edges (including multiedges and loops) and so-called semi-edges. Semi-edges are becoming increasingly popular in modern topological graph theory, as well as in mathematical physics. They also naturally occur in the local computation setting, since they are lifted to matchings in the covering graph. We show that the presence of semi-edges makes the covering problem considerably harder; e.g., it is no longer sufficient to specify the vertex mapping induced by the covering, but one necessarily has to deal with the edge mapping as well. We show some solvable cases and, in particular, completely characterize the complexity of the already very nontrivial problem of covering one- and two-vertex (multi)graphs with semi-edges. Our NP-hardness results are proven for simple input graphs, and in the case of regular two-vertex target graphs, even for bipartite ones. We remark that our new characterization results also strengthen previously known results for covering graphs without semi-edges, and they in turn apply to an infinite class of simple target graphs with at most two vertices of degree more than two. Some of the results are moreover proven in a more general setting (e.g., finding k-tuples of pairwise disjoint perfect matchings in regular graphs, or finding equitable partitions of regular bipartite graphs).
Návaznosti
| GA20-04567S, projekt VaV |
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