784 research outputs found

    Beck's Conjecture for Power Graphs

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    Beck's conjecture on coloring of graphs associated to various algebraic objects has generated considerable interest in the community of discrete mathematics and combinatorics since its inception in the year 1988. The version of this conjecture for power-graphs of finite groups has been addressed and partially settled by previous authors. In this paper we answer it in the affirmative in complete generality, and, in effect, we establish a "nicer" statement on a larger class of graphs. We also clear up certain ambiguities present in the way the previous versions of the conjecture were posed

    Review Of The Future Of College Mathematics Edited By A. Ralston And G. S. Young

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    Keane Leads US Olympiad Team To 1st Place Tie With USSR

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    U.S. Team Places Second In International Olympiad

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    CAMC Examines America

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    The Algorithmic Way Of Life Is Best

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    Complete Multipartite Graphs and the Relaxed Coloring Game

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    Let k be a positive integer, d be a nonnegative integer, and G be a finite graph. Two players, Alice and Bob, play a game on G by coloring the uncolored vertices with colors from a set X of k colors. At all times, the subgraph induced by a color class must have maximum degree at most d. Alice wins the game if all vertices are eventually colored; otherwise, Bob wins. The least k such that Alice has a winning strategy is called the d-relaxed game chromatic number of G, denoted χ gd (G). It is known that there exist graphs such that χ g0 (G) = 3, but χ g1 (G) \u3e 3. We will show that for all positive integers m, there exists a complete multipartite graph G such that m ≤ χ g0 (G) \u3c χ g1 (G)

    Improving Proof-Writing with Reading Guides

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    One of the barriers in the transition to advanced mathematics is that the proofs and ideas in even the best mathematics texts must be read more carefully than many students are accustomed to. Yet in order to learn to write proofs well, one must learn how to read proofs well. Borrowing an idea from Lewis Ludwig, I flipped my introduction to proofs (discrete structures) course in Spring 2016 with the use of reading guides. Each day, students were responsible for reading a section of the text and completing a worksheet that highlighted the main points, asked students to create their own examples of the concepts introduced, and probed the inner workings a proof or two in depth. These reading guides then formed the basis for classroom discussion

    Some Unusual Locus Problems

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