Improved bounds for anti-Ramsey numbers of matchings in outer-planar graphs
نویسندگان
چکیده
Let On be the set of all maximal outer-planar graphs order n. ar(On,F) denote maximum positive integer k such that there is a k-edge-coloring graph T in family which has no rainbow subgraph F. Denote by Mk matching size k. In this paper, we prove ar(On,Mk)≤n+4k−9 for n≥3k−3, expressively improves existing upper bound ar(On,Mk). We also ar(On,M5)=n+4 n≥15.
منابع مشابه
Planar Ramsey Numbers for Small Graphs
Given two graphs G1 and G2, the planar Ramsey number PR(G1, G2) is the smallest integer n such that every planar graph on n vertices either contains a copy of G1 or its complement contains a copy of G2. So far, the planar Ramsey numbers have been determined, when both, G1 and G2 are complete graphs or both are cycles. By combining computer search with some theoretical results, in this paper we ...
متن کاملAnti-Ramsey numbers in complete split graphs
A subgraph of an edge-coloured graph is rainbow if all of its edges have different colours. For graphs G and H the anti-Ramsey number ar(G,H) is the maximum number of colours in an edge-colouring of G with no rainbow copy of H. The notion was introduced by Erdős, Simonovits and V. Sós and studied in case G = Kn. Afterwards exact values or bounds for anti-Ramsey numbers ar(Kn, H) were establishe...
متن کاملUpper Bounds for Perfect Matchings in Pfaffian and Planar Graphs
We give upper bounds on weighted perfect matchings in Pfaffian graphs. These upper bounds are better than generalized Bregman’s inequality. We show that some of our upper bounds are sharp for 3 and 4-regular Pfaffian graphs. We apply our results to fullerene graphs.
متن کاملLocal Anti-Ramsey Numbers of Graphs
In an edge-coloured host graph G, a subgraph H is properly coloured if no two incident edges of H receive the same colour, and rainbow if no two edges of H receive the same colour. Given a positive integer k, a host graph G, an edge-colouring c of G (c is not necessarily proper), then c is a k-colouring if c uses k colours overall, c is a local k-colouring if at most k colours are used at each ...
متن کاملBounds for Ramsey numbers of complete graphs dropping an edge
Let Kn − e be a graph obtained from a complete graph of order n by dropping an edge, and let G p be a Paley graph of order p. It is shown that if G p contains no Kn−e, then r(Kn+1−e) ≥ 2p+1. For example, G1493 contains no K13 − e, so r(K14 − e) ≥ 2987, improving the old bound 2557. It is also shown that r(K2 + G) ≤ 4r(G, K2 + G)− 2, implying that r(Kn − e) ≤ 4 r(Kn−2, Kn − e)− 2. c © 2007 Elsev...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2022
ISSN: ['1873-5649', '0096-3003']
DOI: https://doi.org/10.1016/j.amc.2021.126843