On the anti-ramsey number of forests
Web1 de dez. de 2024 · The anti-Ramsey number A R ( G , H ) of a hypergraph H in a hypergraph G is defined to be the maximum integer k such that there exists a k -edge-coloring of G avoiding rainbow copies of H. The anti-Ramsey numbers of matchings have been extensively studied in several graph classes. But there is few results in … Web1 de fev. de 2024 · The degree anti-Ramsey number A R d (H) of a graph H is the smallest integer k for which there exists a graph G with maximum degree at most k such that any …
On the anti-ramsey number of forests
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Webfor star forests and the approximate value of the anti-Ramsey number for linear forests. Furthermore, we compute the exact value of ar(K n,2P4) for n ≥ 8 and ar(K n,S p,q) for large n, where S p,q is the double star with p+q leaves. Keywords: Anti-Ramsey number, star forest, linear forest, double star. 1. Introduction Let G be a simple ... Web1 de nov. de 2024 · Gorgol [13] considered the anti-Ramsey number of C 3 in complete split graphs and proved the following result. Theorem 3. ([13]) For n ≥ 2, s ≥ 1, ar ( K n + K s ‾, C 3) = n + s − 1. They also gave a lower bound and an upper bound for ar ( K n + K s ‾, C 4) and conjectured that the exact value is closer to the lower bound.
WebThe anti-Ramsey problem was introduced by Erdös, Simonovits, and Sós in 1970s. The anti-Ramsey number of a hypergraph H, ar(n,s, H), is the smallest integer c such that in any coloring of the edges of the s-uniform complete hypergraph on n vertices with exactly c colors, there is a copy of H whose edges have distinct colors. In this paper, we determine … Web7 de set. de 2024 · The anti-Ramsey number is the maximum number of colors in an edge-coloring of with no rainbow copy of . Rainbow coloring of graphs also has its application in practice. It comes from the secure communication of information between agencies of government. The anti-Ramsey number was introduced by Erd s, …
Web1 de fev. de 2024 · The degree anti-Ramsey number A R d (H) of a graph H is the smallest integer k for which there exists a graph G with maximum degree at most k such that any proper edge colouring of G yields a rainbow copy of H.In this paper we prove a general upper bound on degree anti-Ramsey numbers, determine the precise value of the … http://emis.math.tifr.res.in/journals/EJC/Volume_16/PDF/v16i1r85.pdf
Web1 de mai. de 1974 · Abstract. For a graph G, the Ramsey number r ( G) is the smallest natural number p such that given a graph H with p points. H or H̄ contains a G. An ( n,j )-linear forest L is the disjoint union of nontrivial paths, j of which have an odd number of points, and such that the union has n points. If L is an ( n,j )-linear forest, then we show …
WebAnti-Ramsey numbers were introduced by Erd˝os et al. in [5], and showed to be connected not so much to Ramsey theory than to Tur´an numbers. In particular, it was ... Clearly, Ω1 is just the family of forests. In this paper, we consider the anti-Ramsey numbers for … how to restore foam cushionsWeb1 de nov. de 2024 · Abstract. A subgraph of an edge-colored graph is rainbow, if all of its edges have different colors. For a graph G and a family H of graphs, the anti-Ramsey number ar ( G , H ) is the maximum number k such that there exists an edge-coloring of G with exactly k colors without rainbow copy of any graph in H. In this paper, we study the … northeastern army chinaWeb12 de ago. de 2024 · The anti-Ramsey number of a graph in a complete graph , denoted by , is the maximum number of colors in an edge-coloring of with no rainbow subgraph copy … how to restore formula bar in excelWeb3 de jun. de 2015 · The size anti-Ramsey number of H, denoted by AR_s (H), is the smallest number of edges in a graph G such that any of its proper edge-colorings contains a rainbow copy of H. We show that AR_s (K_k) = \varTheta (k^6 / \log ^2 k). This settles a problem of Axenovich, Knauer, Stumpp and Ueckerdt. The proof is probabilistic and … northeastern asa websiteWeb23 de dez. de 2024 · The anti-Ramsey numbers of C3 and C4 in complete r-partite graphs. Discrete Mathematics 2024-11 Journal article DOI: 10. ... On the anti-Ramsey number of forests. Discrete Applied Mathematics 2024-03 Journal article DOI: 10.1016/j.dam.2024.08.027 Contributors ... how to restore font in windows 11Webdetermines the precise value of the degree anti-Ramsey number of every forest. Theorem 1.3. Let F be a forest. Then ARd(F) = e(F) − 1, unless F is a star of any size or a matching withpreciselytwoedges,inwhichcaseARd(F) = e(F). Finally, we study degree anti-Ramsey numbers of cycles. It readily follows from (3) and Corol- how to restore fortigate backup cliWeb1 de fev. de 2024 · PDF We determine the anti-Ramsey numbers for paths. This confirms a conjecture posed by Erdős, Simonovits and Sós in 1970s. Find, read and cite all the research you need on ResearchGate how to restore foggy headlight lens