Graph homomorphisms via vector colorings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10405097" target="_blank" >RIV/00216208:11320/19:10405097 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=b65ZvEyzrY" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=b65ZvEyzrY</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2019.04.001" target="_blank" >10.1016/j.ejc.2019.04.001</a>

Result language
angličtina
Original language name
Graph homomorphisms via vector colorings
Original language description
In this paper we study the existence of homomorphisms G -> H using semidefinite programming. Specifically, we use the vector chromatic number of a graph, defined as the smallest real number t >= 2 for which there exists an assignment of unit vectors i bar right arrow p(i) to its vertices such that < p(i), p(j)> <= -1/(t - 1), when i similar to j. Our approach allows to reprove, without using the Erdos-Ko-Rado Theorem, that for n > 2r the Kneser graph K-n:r and the q-Kneser graph qK(n:r) are cores, and furthermore, that for n/r = n'/r' there exists a homomorphism K-n:r -> K-n':r' if and only if n divides n'. In terms of new applications, we show that the even-weight component of the distance k-graph of the n-cube H-n,H-k is a core and also, that non-bipartite Taylor graphs are cores. Additionally, we give a necessary and sufficient condition for the existence of homomorphisms H-n,(k) -> H-n',H-k' when n/k = n'/k'. Lastly, we show that if a 2-walk-regular graph (which is non-bipartite and not complete multipartite) has a unique optimal vector coloring, it is a core. Based on this sufficient condition we conducted a computational study on Ted Spence's list of strongly regular graphs (http://www.maths.gla.a c.uk/similar to es/srgraphs.php) and found that at least 84% are cores. (C) 2019 Elsevier Ltd. All rights reserved.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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