Geodesic
Characterisation Results for Steiner Triple Systems and Their Application to Edge-Colourings of Cubic Graphs
Canadian journal of mathematics, Tome 62 (2010) no. 2, pp. 355-381

Voir la notice de l'article provenant de la source Cambridge

DOI

It is known that a Steiner triple system is projective if and only if it does not contain the four-triple configuration ${{C}_{14}}$ . We find three configurations such that a Steiner triple system is affine if and only if it does not contain one of these configurations. Similarly, we characterise Hall triple systems using two forbidden configurations.Our characterisations have several interesting corollaries in the area of edge-colourings of graphs. A cubic graph $G$ is $S$ -edge-colourable for a Steiner triple system $S$ if its edges can be coloured with points of $S$ in such a way that the points assigned to three edges sharing a vertex form a triple in $S$ . Among others, we show that all cubic graphs are $S$ -edge-colourable for every non-projective non-affine point-transitive Steiner triple system $S$ .
DOI : 10.4153/CJM-2010-021-9
Mots-clés : 05B07, 05C15 
Král’, Daniel; Máčajová, Edita; Pór, Attila. Characterisation Results for Steiner Triple Systems and Their Application to Edge-Colourings of Cubic Graphs. Canadian journal of mathematics, Tome 62 (2010) no. 2, pp. 355-381. doi: 10.4153/CJM-2010-021-9
@article{10_4153_CJM_2010_021_9,
     author = {Kr\'al{\textquoteright}, Daniel and M\'a\v{c}ajov\'a, Edita and P\'or, Attila},
     title = {Characterisation {Results} for {Steiner} {Triple} {Systems} and {Their} {Application} to {Edge-Colourings} of {Cubic} {Graphs}},
     journal = {Canadian journal of mathematics},
     pages = {355--381},
     year = {2010},
     volume = {62},
     number = {2},
     doi = {10.4153/CJM-2010-021-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-021-9/}
}
TY  - JOUR
AU  - Král’, Daniel
AU  - Máčajová, Edita
AU  - Pór, Attila
TI  - Characterisation Results for Steiner Triple Systems and Their Application to Edge-Colourings of Cubic Graphs
JO  - Canadian journal of mathematics
PY  - 2010
SP  - 355
EP  - 381
VL  - 62
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-021-9/
DO  - 10.4153/CJM-2010-021-9
ID  - 10_4153_CJM_2010_021_9
ER  - 
%0 Journal Article
%A Král’, Daniel
%A Máčajová, Edita
%A Pór, Attila
%T Characterisation Results for Steiner Triple Systems and Their Application to Edge-Colourings of Cubic Graphs
%J Canadian journal of mathematics
%D 2010
%P 355-381
%V 62
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-021-9/
%R 10.4153/CJM-2010-021-9
%F 10_4153_CJM_2010_021_9

Cité par Sources :