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On avoiding and completing coloringsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2019 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Umeå: Umeå University , 2019. , p. 11
##### Series

Research report in mathematics, ISSN 1653-0810 ; 66/19
##### Keywords [en]

Graph coloring, precoloring, list assignment
##### National Category

Discrete Mathematics
##### Identifiers

URN: urn:nbn:se:umu:diva-158343ISBN: 978-91-7855-055-5 (print)OAI: oai:DiVA.org:umu-158343DiVA, id: diva2:1306676
##### Public defence

2019-05-24, MA121, MIT-huset, Umeå, 10:15 (English)
##### Opponent

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt543",{id:"formSmash:j_idt543",widgetVar:"widget_formSmash_j_idt543",multiple:true}); Available from: 2019-05-03 Created: 2019-04-24 Last updated: 2019-04-29Bibliographically approved
##### List of papers

All of my papers are related to the problem of avoiding and completing an edge precoloring of a graph. In more detail, given a graph G and a partial proper edge precoloring φ of G and a list assignment L for every non-colored edge of G, can we extend φ to a proper edge coloring of G which avoids L?

In Paper I, G is the d-dimensional hypercube graph Q_{d}, a partial proper edge precoloring φ and a list assignment L must satisfy certain sparsity conditions. Paper II still deals with the hypercube graph Q_{d}, but the list assignment L for every edge of Q_{d} is an empty set and φ must be a partial proper edge precoloring of at most d-1 edges. In Paper III, G is a (d,s)-edge colorable graph; that is G has a proper d-edge coloring, where every edge is contained in at least s-1 2-colored 4-cycles, L must satisfy certain sparsity conditions and we do not have a partial proper edge precoloring φ on edges of G. The problem in Paper III is also considered in Paper IV and Paper V, but here G can be seen as the complete 3-uniform 3-partite hypergraph K^{3}_{n,n,n}, where n is a power of two in paper IV and n is an even number in paper V.

1. Restricted extension of sparse partial edge colorings of hypercubes$(function(){PrimeFaces.cw("OverlayPanel","overlay1203747",{id:"formSmash:j_idt593:0:j_idt597",widgetVar:"overlay1203747",target:"formSmash:j_idt593:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Edge precoloring extension of hypercubes$(function(){PrimeFaces.cw("OverlayPanel","overlay1203756",{id:"formSmash:j_idt593:1:j_idt597",widgetVar:"overlay1203756",target:"formSmash:j_idt593:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. On restricted colorings of (d,s)-edge colorable graphs$(function(){PrimeFaces.cw("OverlayPanel","overlay1306362",{id:"formSmash:j_idt593:2:j_idt597",widgetVar:"overlay1306362",target:"formSmash:j_idt593:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Latin cubes with forbidden entries$(function(){PrimeFaces.cw("OverlayPanel","overlay1203765",{id:"formSmash:j_idt593:3:j_idt597",widgetVar:"overlay1203765",target:"formSmash:j_idt593:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Latin cubes of even order with forbidden entries$(function(){PrimeFaces.cw("OverlayPanel","overlay1306367",{id:"formSmash:j_idt593:4:j_idt597",widgetVar:"overlay1306367",target:"formSmash:j_idt593:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

isbn
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