2015/10/26 by Żak, Andrzej
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1510.07467
A conjecture by Bollobás from 1995 (which is a weakenning of the famous Tree Packing Conjecture by Gyárfás from 1976) states that any set of k trees Tn,Tn-1,…,Tn-k+1, such that Tn-i has n-i vertices, pack into Kn, provided n is sufficiently large. We confirm Bollobás conjecture for trees Tn,Tn-1,…,Tn-k+1, such that Tn-i has k-1-i leaves or a pending path of order k-1-i. As a consequence we obtain that the conjecture is true for k≤ 5.