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15 papers · 2 filters
Nordhaus-Gaddum-type results for the generalized edge-connectivity of graphs
Xueliang Li, Yaping Mao
Let be a graph, be a set of vertices of , and be the maximum number of pairwise edge-disjoint trees in such that $S\subseteq V…
Decomposition of Triply Rooted Trees
William Y. C. Chen, Janet F. F. Peng, Harold R. L. Yang
In this paper, we give a decomposition of triply rooted trees into three doubly rooted trees. This leads to a combinatorial interpretation of an identity conjectured by Lacasse in…
Rainbow -connectivity of random bipartite graphs
Xiaolin Chen, Xueliang Li, Huishu Lian
A path in an edge-colored graph is called a rainbow path if no two edges of the path are colored the same. The minimum number of colors required to color the edges of such…
On the Maximum Number of k-Hooks of Partitions of n
Anna R. B. Fan, Harold R. L. Yang, Rebecca T. Yu
Let denote the number of -hooks in a partition and let be the maximum value of among partitions of . Amdeberhan posed a conjecture on the gener…
On Pattern Avoiding Alternating Permutations
Joanna N. Chen, William Y. C. Chen, Robin D. P. Zhou
An alternating permutation of length is a permutation such that . Let denote set of alternating permutations of ${1,2,...…
The (revised) Szeged index and the Wiener index of a nonbipartite graph
Lily Chen, Xueliang Li, Mengmeng Liu
Hansen et. al. used the computer programm AutoGraphiX to study the differences between the Szeged index and the Wiener index , and between the revised Szeged index $S…