منابع مشابه
High Girth Cubic Graphs Map to the Clebsch Graph
We give a (computer assisted) proof that the edges of every graph with maximum degree 3 and girth at least 17 may be 5-colored (possibly improperly) so that the complement of each color class is bipartite. Equivalently, every such graph admits a homomorphism to the Clebsch graph (Fig. 1). Hopkins and Staton [8] and Bondy and Locke [2] proved that every (sub)cubic graph of girth at least 4 has a...
متن کاملHigh-girth cubic graphs are homomorphic to the Clebsch graph
We give a (computer assisted) proof that the edges of every graph with maximum degree 3 and girth at least 17 may be 5-colored (possibly improperly) so that the complement of each color class is bipartite. Equivalently, every such graph admits a homomorphism to the Clebsch graph (Fig. 1). Hopkins and Staton [11] and Bondy and Locke [2] proved that every (sub)cubic graph of girth at least 4 has ...
متن کاملSplitting an Expander Graph
Let G V E be an r regular expander graph Certain algorithms for nding edge disjoint paths require the edges of G to be partitioned into E E E Ek so that the graphs Gi V Ei are each expanders In this paper we give a non constructive proof of a very good split plus an algorithm which improves on that given in Broder Frieze and Upfal Existence and construction of edge disjoint paths on expander gr...
متن کاملClebsch-like integrable models
A countable class of integrable dynamical systems, with four dimensional phase space and conserved quantities in involution (Hn, In) are exhibited. For n = 1 we recover Clebsch sytem. All these systems are also integrable at the quantum level.
متن کاملSOME GRAPH PARAMETERS ON THE COMPOSITE ORDER CAYLEY GRAPH
In this paper, the composite order Cayley graph Cay(G, S) is introduced, where G is a group and S is the set of all composite order elements of G. Some graph parameters such as diameter, girth, clique number, independence number, vertex chromatic number and domination number are calculated for the composite order Cayley graph of some certain groups. Moreover, the planarity of composite order Ca...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 1994
ISSN: 0019-3577
DOI: 10.1016/0019-3577(94)90004-3