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2. Graph coloring - Wikipedia

   en.wikipedia.org/wiki/Graph_coloring

   The problem of edge coloring has also been studied in the distributed model. Panconesi & Rizzi (2001) achieve a (2Δ − 1)-coloring in O(Δ + log * n) time in this model. The lower bound for distributed vertex coloring due to Linial (1992) applies to the distributed edge coloring problem as well.

3. Four color theorem - Wikipedia

   en.wikipedia.org/wiki/Four_color_theorem

   In graph-theoretic terms, the theorem states that for loopless planar graph, its chromatic number is ().. The intuitive statement of the four color theorem – "given any separation of a plane into contiguous regions, the regions can be colored using at most four colors so that no two adjacent regions have the same color" – needs to be interpreted appropriately to be correct.

4. Hadwiger–Nelson problem - Wikipedia

   en.wikipedia.org/wiki/Hadwiger–Nelson_problem

   According to Jensen & Toft (1995), the problem was first formulated by Nelson in 1950, and first published by Gardner (1960). Hadwiger (1945) had earlier published a related result, showing that any cover of the plane by five congruent closed sets contains a unit distance in one of the sets, and he also mentioned the problem in a later paper (Hadwiger 1961).

5. Edge coloring - Wikipedia

   en.wikipedia.org/wiki/Edge_coloring

   The road coloring problem is the problem of edge-coloring a directed graph with uniform out-degrees, in such a way that the resulting automaton has a synchronizing word. Trahtman (2009) solved the road coloring problem by proving that such a coloring can be found whenever the given graph is strongly connected and aperiodic.

6. List of NP-complete problems - Wikipedia

   en.wikipedia.org/wiki/List_of_NP-complete_problems

   NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. [3]: ND2 Feedback vertex set [2] [3]: GT7 Feedback arc set [2] [3]: GT8 Graph coloring [2] [3]: GT4

7. The Mathematical Coloring Book - Wikipedia

   en.wikipedia.org/wiki/The_Mathematical_Coloring_Book

   Mathematically, the book considers problems "on the boundary of geometry, combinatorics, and number theory", involving graph coloring problems such as the four color theorem, and generalizations of coloring in Ramsey theory where the use of a too-small number of colors leads to monochromatic structures larger than a single graph edge. [3]