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T-choosability in Graphs by Noga Alon; Ayal Zaks is a Computer Science article available to read on EtoBox.

What is T-choosability in Graphs about?

Given a set of nonnegative integers T. and a function .'/ which assigns a set of integers S(P) to each vertex r of a graph G, an Y-/i.\/ T-co/orim~ L' of G is a vertex-coloring (with positive integers) of G such that c(z')~S( L.) whenever I' E C.(G) and Ic(u) -C(W) t T whenever t LI. w) E E(G). For a fixed T, the T-clzoicr rzunh~r T-ch( G) of a graph G IS the smallest number k such that G has an .Y -list T-coloring for every collection of sets S( (3) of stze X each. Exact values and bounds on the T,.,-choice numbers where T, , = (0.~. 2s.. , K} are presented for even cycles, notably that T,.. ,-ch( Cz,, ) = 2r-t 2 if II > I i I More bounds are obtained by applying algebraic and probabilistic techniques, such as that T-ch(C:,,) <2/ T if 0 E T, and ('II' logtz < T,.,-ch(K,,..) <czrlogn for sonic absolute positive constants cl.(':.

Who reads T-choosability in Graphs?

Author

Noga Alon; Ayal Zaks

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0166-218X)

Published

1998

Language

EN

Field

Computer Science (Physical Sciences)