64 research outputs found
Extended core and choosability of a graph
A graph is -choosable if for any color list of size associated
with each vertices, one can choose a subset of colors such that adjacent
vertices are colored with disjoint color sets. This paper shows an equivalence
between the -choosability of a graph and the -choosability of one
of its subgraphs called the extended core. As an application, this result
allows to prove the -choosability and -colorability of
triangle-free induced subgraphs of the triangular lattice.Comment: 10 page
Choosability of a weighted path and free-choosability of a cycle
A graph with a list of colors and weight for each vertex
is -colorable if one can choose a subset of colors from
for each vertex , such that adjacent vertices receive disjoint color
sets. In this paper, we give necessary and sufficient conditions for a weighted
path to be -colorable for some list assignments . Furthermore, we
solve the problem of the free-choosability of a cycle.Comment: 9 page
On List-Coloring and the Sum List Chromatic Number of Graphs.
This thesis explores several of the major results in list-coloring in an expository fashion. As a specialization of list coloring, the sum list chromatic number is explored in detail. Ultimately, the thesis is designed to motivate the discussion of coloring problems and, hopefully, interest the reader in the branch of coloring problems in graph theory
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