منابع مشابه
Cyclically decomposing the complete graph into cycles
Let m1; m2; : : : ; mk be positive integers not less than 3 and let n= ∑k i=1 mi. Then, it is proved that the complete graph of order 2n+ 1 can be cyclically decomposed into k(2n+ 1) cycles such that, for each i= 1; 2; : : : ; k, the cycle of length mi occurs exactly 2n+ 1 times. c © 2003 Elsevier B.V. All rights reserved.
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The cycle-complete graph Ramsey number r (Cm,Kn ) is the smallest integer N such that every graph G of order N contains a cycle Cm on m vertices or has independence number (G) n. It has been conjectured by Erdős, Faudree, Rousseau and Schelp that r (Cm,Kn )1⁄4 (m 1) (n 1)þ 1 for all m n 3 (except r (C3,K3 )1⁄4 6). This conjecture holds for 3 n 5: In this paper we will present a proof for n 1⁄4 ...
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A d-graph G = (V ;E1, . . . , Ed) is a complete graph whose edges are colored by d colors, or in other words, are partitioned into d subsets (some of which might be empty). We say that G is complementary connected if the complement to each chromatic component of G is connected on V , or in other words, if for each two vertices u, w ∈ V and color i ∈ I = {1, . . . , d} there is a path between u ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2018
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2017.08.008