Unbalanced star-factorisations of complete bipartite graphs
نویسندگان
چکیده
منابع مشابه
A Family of Perfect Factorisations of Complete Bipartite Graphs
A 1-factorisation of a graph is perfect if the union of any two of its 1-factors is a Hamiltonian cycle. Let n=p for an odd prime p. We construct a family of (p−1)/2 non-isomorphic perfect 1-factorisations of Kn, n. Equivalently, we construct pan-Hamiltonian Latin squares of order n. A Latin square is pan-Hamiltonian if the permutation defined by any row relative to any other row is a single cy...
متن کاملMETA-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...
متن کاملIsomorphic Factorisations . I : Complete Graphs
An isomorphic factorisation of the complete graph Kj, is a partition of the lines of Kp into t isomorphic spanning subgraphs G; we then write G\Kj, and G G K^/t. If the set of graphs Ky/t is not empty, then of course t\p(p — l)/2. Our principal purpose is to prove the converse. It was found by Laura Guidotti that the converse does hold whenever (/,/>) » 1 or (t,p — 1) «= 1, We give a new and sh...
متن کاملForcing unbalanced complete bipartite minors
Myers conjectured that for every integer s there exists a positive constant C such that for all integers t every graph of average degree at least Ct contains a Ks,t minor. We prove the following stronger result: for every 0 < ε < 10−16 there exists a number t0 = t0(ε) such that for all integers t ≥ t0 and s ≤ εt/ log t every graph of average degree at least (1 + ε)t contains a Ks,t minor. The b...
متن کاملMixed cycle-E-super magic decomposition of complete bipartite graphs
An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ΣνεV(H) f(v) + ΣeεE(H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥ ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2004
ISSN: 0012-365X
DOI: 10.1016/j.disc.2004.01.003