(UL)
-
On a relation between bipartite biregular cages, block designs and generalized polygonsAraujo-Pardo, Gabriela ...A bipartite biregular ▫$(m,n;g)$▫-graph ▫$\Gamma$▫ is a bipartite graph of even girth ▫$g$▫ having the degree set ▫$\{m,n\}$▫ and satisfying the additional property that the vertices in the same ... partite set have the same degree. An ▫$(m,n;g)$▫-bipartite biregular cage is a bipartite biregular ▫$(m,n;g)$▫-graph of minimum order. In their 2019 paper, Filipovski, Ramos-Rivera, and Jajcay present lower bounds on the orders of bipartite biregular ▫$(m,n;g)$▫-graphs, and call the graphs that attain these bounds bipartite biregular Moore cages. In our paper, we improve the lower bounds obtained in the above paper. Furthermore, in parallel with the well-known classical results relating the existence of ▫$k$▫-regular Moore graphs of even girths ▫$g=6$▫, ▫$8$▫, and ▫$12$▫ to the existence of projective planes, generalized quadrangles, and generalized hexagons, we prove that the existence of an ▫$S(2,k,v)$▫-Steiner system yields the existence of a bipartite biregular ▫$(k, {v−1 \over k−1} ;6)$▫-cage, and, vice versa, the existence of bipartite biregular ▫$(k,n;6)$▫-cage whose order is equal to one of our lower bounds yields the existence of an ▫$S(2,k,1+n(k−1))$▫-Steiner system. Moreover, with regard to the special case of Steiner triple systems, we completely solve the problem of determining the orders of ▫$(3,n;6)$▫-bipartite biregular cages for all integers ▫$n \ge 4$▫. Considering girths higher than ▫$6$▫, we relate the existence of generalized polygons (quadrangles, hexagons, and octagons) to the existence of ▫$(n+1,n^2+1;8)$▫-, ▫$(n^2+1,n^3+1;8)$▫-, ▫$(n,n+2;8)$▫-, ▫$(n+1,n^3+1;12)$▫- and ▫$(n+1,n^2+1;16)$▫-bipartite biregular cages, respectively. Using this connection, we also derive improved upper bounds for the orders of other classes of bipartite biregular cages of girths ▫$8$▫, ▫$12$▫, and ▫$14$▫.Source: Journal of combinatorial designs. - ISSN 1063-8539 (Vol. 30, iss. 7, July 2022, str. 479-496)Type of material - article, component part ; adult, seriousPublish date - 2022Language - englishCOBISS.SI-ID - 159759875
source: Journal of combinatorial designs. - ISSN 1063-8539 (Vol. 30, iss. 7, July 2022, str. 479-496)
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 |
---|---|
Araujo-Pardo, Gabriela | |
Jajcay, Robert | 37724 |
Ramos Rivera, Alejandra | 37541 |
Szőnyi, Tamás | 51192 |
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: