Linearna razvejanost ▫${\rm la}(G)$▫ grafa ▫$G$▫ je najmanjše število linearnih gozdov (grafov, v katerih je vsaka povezana komponenta pot), ki delijo povezave ▫$G$▫. Leta 1984 so Akiyama et al. ...podali hipotezo o linearni razvejanosti (Linear Arboricity Conjecture (LAC)), ki pravi, da je linearna razvejanost poljubnega enostavnega grafa z maksimalno stopnjo ▫$\Delta$▫ ali ▫$\big \lceil \tfrac{\Delta}{2} \big \rceil$ ali $\big \lceil \tfrac{\Delta+1}{2} \big \rceil$▫. Dokazano je že, da LAC drži za vse ravninske grafe. Iz LAC sledi, da za lihe ▫$\Delta$▫ velja ▫${\rm la}(G)=\big \lceil \tfrac{\Delta}{2} \big \rceil$▫. V članku postavimo hipotezo, ki pravi, da je zgornja enakost resnična tudi za vse sode ▫$\Delta \ge 6$▫. Dokazali smo, da drži za vse sode ▫$\Delta \ge 10$▫. Odprto ostane vprašanje za ▫$\Delta=6, 8$▫. Predstavimo tudi algoritem s časovno zahtevnostjo ▫$O(n\log n)$▫, ki razdeli ravninski graf na ▫$\max\{{\rm la}(G), 5\}$▫ linearnih gozdov, ki je optimalen za ▫$\Delta \ge 9$▫.
It was not necessary to add the material to the shelf.
Bibliographic material was successfully added on shelf.
Adding bibliographical material on shelf was not successful.
Material is already on the shelf.
Permalink
URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year
Impact factor
Edition
Category
Classification
JCR
SNIP
JCR
SNIP
JCR
SNIP
JCR
SNIP
Select the library membership card:
DRS,
in which the journal is indexed
Database name
Field
Year
Links to authors' personal bibliographies
Links to information on researchers in the SICRIS system
Subject headings in COBISS General List of Subject Headings
Select pickup location
The material from the parent unit is free. If the material is delivered to the pickup location from another unit, the library may charge you for this service.
