Drago Bokal (Avtor), Markus Chimani (Avtor), Jesús Leanõs (Avtor)

Povzetek

Consider a graph ▫$G$▫ with a minimal edge cut ▫$F$▫ and let ▫$G_1$▫, ▫$G_2$▫ be the two (augmented) components of ▫$G-F$▫. A long-open question asks under which conditions the crossing number of ▫$G$▫ is (greater than or) equal to the sum ofcthe crossing numbers of ▫$G_1$▫ and ▫$G_2$▫ - which would allow us to consider those graphs separately. It is known that crossing number is additive for ▫$|F| \in \{0,1,2\}$▫ and that there exist graphs violating this property with ▫$|F| \ge 4$▫. In this paper, we show that crossing number is additive for ▫$|F|=3$▫, thus closing the final gap in the question. The techniques generalize to show that minor crossing number is additive over edge cuts of arbitrary size, as well as to provide bounds for crossing number additivity in arbitrary surfaces. We point out several applications to exact crossing number computation and crossing-critical graphs, as well as provide a very general lower bound for the minor crossing number of the Cartesian product of an arbitrary graph with a tree.

Ključne besede

matematika;teorija grafov;prekrižno število;minor;mathematics;graph theory;crossing number;

Podatki

Jezik: Angleški jezik
Leto izida:
Tipologija: 1.01 - Izvirni znanstveni članek
Organizacija: UM FNM - Fakulteta za naravoslovje in matematiko
UDK: 519.17
COBISS: 16624473 Povezava se bo odprla v novem oknu
ISSN: 0195-6698
Št. ogledov: 35
Št. prenosov: 22
Ocena: 0 (0 glasov)
Metapodatki: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Ostali podatki

Sekundarni jezik: Angleški jezik
Sekundarne ključne besede: matematika;teorija grafov;prekrižno število;minor;
URN: URN:SI:UM:
Vrsta dela (COBISS): Delo ni kategorizirano
Strani: str. 1010-1018
Letnik: Vol. 34
Zvezek: iss. 6
Čas izdaje: 2013
ID: 1476829