منابع مشابه
High-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 کاملHigh 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 کاملSymmetric cubic graphs of small girth
A graph Γ is symmetric if its automorphism group acts transitively on the arcs of Γ, and s-regular if its automorphism group acts regularly on the set of s-arcs of Γ. Tutte (1947, 1959) showed that every cubic finite symmetric cubic graph is s-regular for some s ≤ 5. We show that a symmetric cubic graph of girth at most 9 is either 1-regular or 2-regular (following the notation of Djokovic), or...
متن کاملDomination in Cubic Graphs of Large Girth
We prove that connected cubic graphs of order n and girth g have domination number at most 0.32127n+O ( n g ) .
متن کاملThe Smallest Cubic Graphs of Girth Nine
We describe two computational methods for the construction of cubic graphs with given girth. These were used to produce two independent proofs that the (3, 9)-cages, defined as the smallest cubic graphs of girth 9, have 58 vertices. There are exactly 18 such graphs. We also show that cubic graphs of girth 11 must have at least 106 vertices and cubic graphs of girth 13 must have at least 196 ver...
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ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 1960
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-1960-018-1