Matrix Choosability
نویسندگان
چکیده
منابع مشابه
Matrix Choosability
Let F be a finite field with pc elements, let A be a n×n matrix over F , and let k be a positive integer. When is it true that for all X1, . . . , Xn ⊆ F with |Xi| = k+1 and for all Y1, . . . , Yn ⊆ F with |Yi| = k, there exist x ∈ X1×. . .×Xn and y ∈ (F \Y1)×. . .×(F \Yn) such that Ax = y? It is trivial that A has this property for k = pc − 1 if det(A) 6= 0. The permanent lemma of Noga Alon pr...
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The adaptable choosability number of a multigraph G, denoted cha(G), is the smallest integer k such that every edge labeling of G and assignment of lists of size k to the vertices of G permits a list coloring of G in which no edge e = uv has both u and v colored with the label of e. We show that cha grows with ch, i.e. there is a function f tending to infinity such that cha(G) ≥ f(ch(G)).
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It is proved that a planar graph G without five cycles is three degenerate, hence, four choosable, and it is also edge-(A( G) + l)h c oosable. @ 2002 Elsevier Science Ltd. All rights reserved. Keywords-Choosability, Edge choosability, Degeneracy, Planar graph.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2000
ISSN: 0097-3165
DOI: 10.1006/jcta.1999.3026