(UL)
-
A minimum degree condition forcing complete graph immersionDeVos, Matt ...An immersion of a graph ▫$H$▫ into a graph ▫$G$▫ is a one-to-one mapping ▫$f:V(H) \to V(G)$▫ and a collection of edge-disjoint paths in ▫$G$▫, one for each edge of ▫$H$▫, such that the path ... ▫$P_{uv}$▫ corresponding to edge ▫$uv$▫ has endpoints ▫$f(u)$▫ and ▫$f(v)$▫. The immersion is strong if the paths ▫$P_{uv}$▫ are internally disjoint from ▫$f(V(H))$▫. It is proved that for every positive integer ▫$t$▫, every simple graph of minimum degree at least ▫$200t$▫ contains a strong immersion of the complete graph ▫$K_t$▫. For dense graphs one can say even more. If the graph has order ▫$n$▫ and has ▫$2cn^2$▫ edges, then there is a strong immersion of the complete graph on at least ▫$c^2 n$▫ vertices in ▫$G$▫ in which each path ▫$P_{uv}$▫ is of length 2. As an application of these results, we resolve a problem raised by Paul Seymour by proving that the line graph of every simple graph with average degree ▫$d$▫ has a clique minor of order at least ▫$cd^{3/2}$▫, where▫ $c>0$▫ is an absolute constant. For small values of ▫$t$▫, ▫$1 \le t \le 7$▫, every simple graph of minimum degree at least ▫$t-1$▫ contains an immersion of ▫$K_t$▫ (Lescure and Meyniel, DeVos et al.). We provide a general class of examples showing that this does not hold when ▫$t$▫ is large.Source: Combinatorica. - ISSN 0209-9683 (Vol. 34, no. 3, 2014, str. 279-298)Type of material - article, component part ; adult, seriousPublish date - 2014Language - englishCOBISS.SI-ID - 17210969
Author
DeVos, Matt |
Dvořák, Zdeněk |
Fox, Jacob |
McDonald, Jessica |
Mohar, Bojan, 1956- |
Scheide, Diego
Topics
matematika |
teorija grafov |
imerzija |
polni grafi |
mathematics |
graph theory |
complete graph immersion
![loading ... loading ...](themes/default/img/ajax-loading.gif)
Shelf entry
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:
If the library membership card is not in the list,
add a new one.
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 |
---|---|
DeVos, Matt | ![]() |
Dvořák, Zdeněk | ![]() |
Fox, Jacob | ![]() |
McDonald, Jessica | ![]() |
Mohar, Bojan, 1956- | 01931 |
Scheide, Diego | ![]() |
Source: Personal bibliographies
and: SICRIS
Select pickup location:
Material pickup by post
Delivery address:
Address is missing from the member's data.
The address retrieval service is currently unavailable, please try again.
By clicking the "OK" button, you will confirm the pickup location selected above and complete the reservation process.
By clicking the "OK" button, you will confirm the above pickup location and delivery address, and complete the reservation process.
By clicking the "OK" button, you will confirm the address selected above and complete the reservation process.
Notification
Automatic login and reservation service currently not available. You can reserve the material on the Biblos portal or try again here later.
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.
Pickup location | Material status | Reservation |
---|
Reservation in progress
Please wait a moment.
Reservation was successful.
Reservation failed.
Reservation...
Membership card:
Pickup location: