Geodesic
Flows on the join of two graphs
Mathematica Bohemica, Tome 138 (2013) no. 4, pp. 383-396.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

The join of two graphs $G$ and $H$ is a graph formed from disjoint copies of $G$ and $H$ by connecting each vertex of $G$ to each vertex of $H$. We determine the flow number of the resulting graph. More precisely, we prove that the join of two graphs admits a nowhere-zero $3$-flow except for a few classes of graphs: a single vertex joined with a graph containing an isolated vertex or an odd circuit tree component, a single edge joined with a graph containing only isolated edges, a single edge plus an isolated vertex joined with a graph containing only isolated vertices, and two isolated vertices joined with exactly one isolated vertex plus some number of isolated edges.
DOI : 10.21136/MB.2013.143511
Classification : 05C21
Keywords: nowhere-zero flow; graph join 
@article{10_21136_MB_2013_143511,
     author = {Luko\v{t}ka, Robert and Rollov\'a, Edita},
     title = {Flows on the join of two graphs},
     journal = {Mathematica Bohemica},
     pages = {383--396},
     publisher = {mathdoc},
     volume = {138},
     number = {4},
     year = {2013},
     doi = {10.21136/MB.2013.143511},
     mrnumber = {3231093},
     zbl = {06260039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143511/}
}
TY  - JOUR
AU  - Lukoťka, Robert
AU  - Rollová, Edita
TI  - Flows on the join of two graphs
JO  - Mathematica Bohemica
PY  - 2013
SP  - 383
EP  - 396
VL  - 138
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143511/
DO  - 10.21136/MB.2013.143511
LA  - en
ID  - 10_21136_MB_2013_143511
ER  - 
%0 Journal Article
%A Lukoťka, Robert
%A Rollová, Edita
%T Flows on the join of two graphs
%J Mathematica Bohemica
%D 2013
%P 383-396
%V 138
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143511/
%R 10.21136/MB.2013.143511
%G en
%F 10_21136_MB_2013_143511
Lukoťka, Robert; Rollová, Edita. Flows on the join of two graphs. Mathematica Bohemica, Tome 138 (2013) no. 4, pp. 383-396. doi : 10.21136/MB.2013.143511. http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143511/

Cité par Sources :