Some results on double triangle descendants of K 5
Annales de l’Institut Henri Poincaré D, Tome 8 (2021) no. 4, pp. 537-581.
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez l'article sur le site de la revue.

Double triangle expansion is an operation on 4-regular graphs with at least one triangle which replaces a triangle with two triangles in a particular way. We study the class of graphs which can be obtained by repeated double triangle expansion beginning with the complete graph K 5 . These are called double triangle descendants of K 5 . We enumerate, with explicit rational generating functions, those double triangle descendants of K 5 with at most four more vertices than triangles. We also prove that the minimum number of triangles in any K 5 descendant is four. Double triangle descendants are an important class of graphs because of conjectured properties of their Feynman periods when they are viewed as scalar Feynman diagrams, and also because of conjectured properties of their c 2 invariants, an arithmetic graph invariant with quantum field theoretical applications.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/110
Classification : 05-XX, 81-XX
Mots-clés : Double triangle reduction/expansion, $K_5$-descendants, zigzags, $n$-zigzags, $\phi^4$ theory, constant $c_2$-invariant. 
@article{AIHPD_2021__8_4_537_0,
     author = {Laradji, Mohamed and Mishna, Marni and Yeats, Karen},
     title = {Some results on double triangle descendants of $K_5$},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {537--581},
     volume = {8},
     number = {4},
     year = {2021},
     doi = {10.4171/aihpd/110},
     mrnumber = {4337448},
     zbl = {1479.05156},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/aihpd/110/}
}
TY  - JOUR
AU  - Laradji, Mohamed
AU  - Mishna, Marni
AU  - Yeats, Karen
TI  - Some results on double triangle descendants of $K_5$
JO  - Annales de l’Institut Henri Poincaré D
PY  - 2021
SP  - 537
EP  - 581
VL  - 8
IS  - 4
UR  - http://www.numdam.org/articles/10.4171/aihpd/110/
DO  - 10.4171/aihpd/110
LA  - en
ID  - AIHPD_2021__8_4_537_0
ER  - 
%0 Journal Article
%A Laradji, Mohamed
%A Mishna, Marni
%A Yeats, Karen
%T Some results on double triangle descendants of $K_5$
%J Annales de l’Institut Henri Poincaré D
%D 2021
%P 537-581
%V 8
%N 4
%U http://www.numdam.org/articles/10.4171/aihpd/110/
%R 10.4171/aihpd/110
%G en
%F AIHPD_2021__8_4_537_0
Laradji, Mohamed; Mishna, Marni; Yeats, Karen. Some results on double triangle descendants of $K_5$. Annales de l’Institut Henri Poincaré D, Tome 8 (2021) no. 4, pp. 537-581. doi : 10.4171/aihpd/110. http://www.numdam.org/articles/10.4171/aihpd/110/

Cité par Sources :