TY  - JOUR
ID  - Cary2019
LB  - Cary2019
AU  - Cary, Michael
TI  - Vertices with the second neighborhood property in Eulerian digraphs
ST  - Vertices with the second neighborhood property in Eulerian digraphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2019
VL  - 39
IS  - 6
SP  - 765
EP  - 772
DO  - https://doi.org/10.7494/OpMath.2019.39.6.765
UR  - https://doi.org/10.7494/OpMath.2019.39.6.765
AB  - The Second Neighborhood Conjecture states that every simple digraph has a vertex whose second out-neighborhood is at least as large as its first out-neighborhood, i.e. a vertex with the Second Neighborhood Property. A cycle intersection graph of an even graph is a new graph whose vertices are the cycles in a cycle decomposition of the original graph and whose edges represent vertex intersections of the cycles. By using a digraph variant of this concept, we prove that Eulerian digraphs which admit a simple cycle intersection graph not only adhere to the Second Neighborhood Conjecture, but that local simplicity can, in some cases, also imply the existence of a Seymour vertex in the original digraph.
KW  - Eulerian digraph
KW  - second neighborhood conjecture
KW  - cycle decomposition
KW  - cycle intersection graph
SN  - 1232-9274
ER  -