Partitions of bipartite numbers

Bipartite regulation numbers

✍ Yousef Alavi; Gary Chartrand; Ortrud R Oellermann; Linda Lesniak 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 371 KB

The bipartite regulation number br(G) of a bipartite graph G with maximum degree d is the minimum number of vertices required to add to G to construct a d-regular bipartite by-n bipartite graph with m <~ n and n -m >~ d -1, then br(G) = n -m. If, however, n -m ~< d -2, then br(G) = n -m + 2/for som

Bipartite anti-Ramsey numbers of cycles

✍ Maria Axenovich; Tao Jiang; André Kündgen 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 265 KB

## Abstract We determine the maximum number of colors in a coloring of the edges of __K~m,n~__ such that every cycle of length 2__k__ contains at least two edges of the same color. One of our main tools is a result on generalized path covers in balanced bipartite graphs. For positive integers __q__

Star-path bipartite Ramsey numbers

✍ Johannes H. Hattingh; Michael A. Henning 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 213 KB

For bipartite graphs G1,G2 ..... Gk, the bipartite Ramsey number b(GI,G2,...,Gk) is the least positive integer b so that any colouring of the edges of Kb, b with k colours will result in a copy of Gi in the ith colour for some i. In this note, we establish the exact value of the bipartite Ramsey num

Circular Numbers andn-set Partitions

✍ Daniel N. Port 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 426 KB

Partitions of n-sets and their associated Bell and Stirling numbers are wellstudied combinatorial entities. Less studied is the connection between these entities and the moments of a Poisson random variable. We find a natural generalization of this connection by considering the moments of the circul

Partitions into two Lehmer numbers

✍ Igor E. Shparlinski; Arne Winterhof 📂 Article 📅 2009 🏛 Springer Vienna 🌐 English ⚖ 158 KB

A bipartite Ramsey number

✍ Geoffrey Exoo 📂 Article 📅 1991 🏛 Springer Japan 🌐 English ⚖ 101 KB