Characterisation Results for Steiner Triple Systems and Their
Application to Edge-Colourings of Cubic Graphs

J 2010

Characterisation Results for Steiner Triple Systems and Their Application to Edge-Colourings of Cubic Graphs

KRÁĽ, Daniel; E MACAJOVA; A POR a JS SERENI

Základní údaje

Originální název

Characterisation Results for Steiner Triple Systems and Their Application to Edge-Colourings of Cubic Graphs

Autoři

KRÁĽ, Daniel; E MACAJOVA; A POR a JS SERENI

Vydání

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, OTTAWA, CANADIAN MATHEMATICAL SOCIETY, 2010, 0008-414X

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 0.776

Označené pro přenos do RIV

DOI

https://doi.org/10.4153/CJM-2010-021-9

UT WoS

000275983400007

Změněno: 6. 11. 2020 09:36, Mgr. Darina Boukalová

Anotace

V originále

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.

Citovat

KRÁĽ, Daniel; E MACAJOVA; A POR a JS SERENI. Characterisation Results for Steiner Triple Systems and Their Application to Edge-Colourings of Cubic Graphs. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES. OTTAWA: CANADIAN MATHEMATICAL SOCIETY, 2010, roč. 62, č. 2, s. 355-381. ISSN 0008-414X. Dostupné z: https://doi.org/10.4153/CJM-2010-021-9.

@article{1689654,
   author = {Kráľ, Daniel and Macajova, E and Por, A and Sereni, JS},
   article_location = {OTTAWA},
   article_number = {2},
   doi = {https://doi.org/10.4153/CJM-2010-021-9},
   language = {eng},
   issn = {0008-414X},
   journal = {CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES},
   title = {Characterisation Results for Steiner Triple Systems and Their Application to Edge-Colourings of Cubic Graphs},
   volume = {62},
   year = {2010}
}

TY  - JOUR
ID  - 1689654
AU  - Kráľ, Daniel - Macajova, E - Por, A - Sereni, JS
PY  - 2010
TI  - Characterisation Results for Steiner Triple Systems and Their Application to Edge-Colourings of Cubic Graphs
JF  - CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
VL  - 62
IS  - 2
SP  - 355-381
EP  - 355-381
PB  - CANADIAN MATHEMATICAL SOCIETY
SN  - 0008414X
N2  - 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.
ER  -

KRÁĽ, Daniel; E MACAJOVA; A POR a JS SERENI. Characterisation Results for Steiner Triple Systems and Their Application to Edge-Colourings of Cubic Graphs. \textit{CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES}. OTTAWA: CANADIAN MATHEMATICAL SOCIETY, 2010, roč.~62, č.~2, s.~355-381. ISSN~0008-414X. Dostupné z: https://doi.org/10.4153/CJM-2010-021-9.

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