High-girth cubic graphs are homomorphic to the Clebsch graph
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چکیده
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...
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Let G be a graph and let c : V (G) → ({1,...,5} 2 ) be an assignment of 2-element subsets of the set {1, . . . , 5} to the vertices of G such that for every edge vw, the sets c(v) and c(w) are disjoint. We call such an assignment a (5, 2)-coloring. A graph is (5,2)-colorable if and only if it has a homomorphism to the Petersen graph. The odd-girth of a graph G is the length of the shortest odd ...
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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: Journal of Graph Theory
سال: 2011
ISSN: 0364-9024
DOI: 10.1002/jgt.20580