Gabriela Araujo-Pardo

Finding small regular graphs of girths 6, 8 and 12 as subgraphs of cages

Small k-regular graphs of girth g where g=6,8,12 are obtained as subgraphs of minimal cages. More precisely, we obtain (k,6)-graphs on 2(kq-1) vertices, (k,8)-graphs on 2k(q^2-1) vertices and (k,12)-graphs on 2kq^2(q^2-1), where q is a prime power and k is a positive integer such that q>=k>=3. Some of these graphs have the smallest number of vertices known so far among the regular graphs with girth g=6,8,12.

Constructions of small regular bipartite graphs of girth 6

In this article, some structures in the projective plane of order

A conjecture of Neumann-Lara on infinite families of r-dichromatic circulant tournaments

q

On the order of ({r,m};g)-cages of even girth

**image** are found which allow us to construct small

Families of small regular graphs of girth 5

k

Colorful associahedra and cyclohedra

**image** -regular balanced bipartite graphs of girth 6 for all

On upper bounds of odd girth cages

k\le q

Constructions of biregular cages of girth five

**image** . When

The ωψ-perfection of graphs

k=q

On upper bounds and connectivity of cages

**image** , the order of these