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Showing 1 to 14 of 14 for “"list coloring"”.
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List coloring in general graphs
… the relatively new approaches to the problem of list-coloring graphs. This is a problem that has its roots in classical graph theory, but has developed an entire theory of its own, that uses tools from structural graph theory, probabilistic approaches, as well as heuristic and algorithmic …
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Problems in list coloring, triangle covering, and pursuit-evasion games
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2014-07-14T16:02:09Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 11 littletuza.tex: 12675 bytes, checksum: addf3766f19108432eeb6fc23765de37 (MD5) uiucthesis2009.cls: 17082 bytes, checksum: …
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Equitable List Coloring, Induced Linear Forests, and Routing in Rooted Graphs
We explicitly characterize the family of networks for which such a protocol exists. This characterization is given in terms of forbidden rooted minors, which leads to a linear time recognition algorithm for this family of networks. We obtain a similar characterization for the family of networks in …
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Coloring problems in graph theory
<p>We consider two branches of coloring problems for graphs: list coloring and packing coloring. We introduce a new variation to list coloring which we call choosability with union separation: For a graph G, a list assignment L to the vertices of G is a (k,k+t)-list assignment if every vertex is …
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Coloring and constructing (hyper)graphs with restrictions
… existence of graphs and hypergraphs with certain coloring properties and other structural properties. In Chapter 2 we consider color-critical graphs that are nearly bipartite and have few edges. We prove a conjecture of Chen, Erdős, Gyárfás, and Schelp concerning the minimum number of edges in a …
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Small cycle cover, group coloring with related problems
… Linial, Payan and Tarsi introduced group coloring in 1992 and proved that the group chromatic number for every planar graph is at most 6. It is shown that the bound 6 can be decreased to 5. Jaeger, Linial, Payan and Tarsi also proved that the group chromatic number for every planar graph …
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An Introduction to List Colorings of Graphs
… and useful areas of graph theory is graph colorings. A graph coloring is an assignment of integers to the vertices of a graph so that no two adjacent vertices are assigned the same integer. This problem frequently arises in scheduling and channel assignment applications. A list coloring of …
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Coloring problems in combinatorics and descriptive set theory
In this dissertation we study problems related to colorings of combinatorial structures both in the “classical” finite context and in the framework of descriptive set theory, with applications to topological dynamics and ergodic theory. This work consists of two parts, each of which is in turn …
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Decay of correlations and inference in graphical models
… We consider three specific problems: 1) The List Coloring problem on graphs, [upper case letter g in italic] The MAX-CUT problem on graphs with random edge deletions, and 3) Low Rank Matrix Completion from an incomplete subset of its entries. For each problem, we analyze the conditions under …
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Online choosability of graphs
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2015-09-29 without embargo terms
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Colorings and list colorings of graphs and hypergraphs
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-04-04T13:50:38Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 3 thesis.tex: 208138 bytes, checksum: 3f2bbfe42b155982f3fe9f0f51b4e863 (MD5) config1.eps: 12369 bytes, checksum: …
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Coloring and covering problems on graphs
… A \emph{star $k$-coloring} is a proper $k$-coloring where the union of any two color classes induces a star forest. While every planar graph is 4-colorable, not every planar graph is star 4-colorable. One method to produce a star 4-coloring is to partition the …
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Graphs, codes, and colorings
Item withdrawn by Alexis Thompson (athmpsn1@illinois.edu) on 2010-11-24T20:52:49Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Kantor_Ida.pdf: 588064 bytes, checksum: ed396002d8eb12e47e04cf8040eb7e99 (MD5)
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Games on graphs, visibility representations, and graph colorings
… digraphs with b(D)=1. A proper vertex coloring of a graph G is r-dynamic if for each v ∈ V (G), at least min{r, d(v)} colors appear in N_G(v). We investigate r-dynamic versions of coloring and list coloring. We give upper bounds on the minimum number of colors needed for any r in terms …