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math.CO2016
Gallai's path decomposition conjecture for graphs of small maximum degree
Marthe Bonamy, Thomas Perrett
Gallai's path decomposition conjecture states that the edges of any connected graph on n vertices can be decomposed into at most (n+1)/2 paths. We confirm that conjecture for all g…
math.CO2016★ 13 cited
On the difference between the Szeged and Wiener index
Marthe Bonamy, Martin Knor, Borut Lužar +2
We prove a conjecture of Nadjafi-Arani, Khodashenas and Ashrafi on the difference between the Szeged and Wiener index of a graph. Namely, if is a 2-connected non-complete graph…