MATH 360 Spring 2023
Combinatorics and Graph Theory
Archived Class
Charles Cusack
Mathematics and Statistics
Hope College
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Schedule for weeks 1 through 16

Wk Day Date TopicResourcesEvents

1TueJan 10
  • Course Introduction
  • Graphs
  • Graph Terminology
  • CGT 1-1.1.21.1.1: 3,4
    1.1.2: 1,2,4,5,9, 12,15,16

    ThuJan 12Special Types of GraphsCGT 1.1.31.1.3: 1,5,6,8,9,10

    2TueJan 17Distance in GraphsCGT 1.21.2.1: 1,2,6,8,11
    1.2.2: 1,2,4,6
    1.2.3: 2,3

    ThuJan 19TreesCGT 1.3-1.3.3HW 1 due
    1.3.1: 1,2,3
    1.3.2: 1,3,5,8
    1.3.3: 1,4,5,7

    3TueJan 24Counting TreesCGT 1.3.41.3.4: 2,3,4,5,6

    ThuJan 26Trails, Circuits, Paths, and CyclesCGT 1.4-1.4.2HW 2 due
    1.4.1: 2,3
    1.4.2: 1,2,4,5,7,8

    4TueJan 31
  • Hamiltonian Paths and Cycles
  • Three Open Problems
  • CGT 1.4.3-1.4.4HW 3 due
    1.4.3: 1,4,6,7,9,12
    1.4.4: 1,2,3,4

    ThuFeb 02
  • Planarity
  • Euler's Formula and Beyond
  • CGT 1.5-1.5.21.5.1: 1,2,5,6,8
    1.5.2: 1,2,4,7,9,10
    Note: add "with triangular regions" to 10. (typo)

    5TueFeb 07
  • Regular Polyhedra
  • Kuratowski's Theorem
  • CGT 1.5.3-1.5.4HW 4 due
    1.5.3: 1,2
    1.5.4: 1,2,4

    ThuFeb 09ColoringsCGT 1.6-1.6.21.6.1: 1,2,4,5
    1.6.2: 2,5,6,7

    6TueFeb 14No ClassWinter Recess

    ThuFeb 16
  • The Four Color Problem
  • Chromatic Polynomials
  • CGT 1.6.3-1.6.41.6.3: 1,3,5
    1.6.4: 1,3,4

    7TueFeb 21
  • Matchings
  • Hall's Theorem and SDRs
  • CGT 1.7-1.7.2HW 5 due
    1.7.1: 1,2
    1.7.2: 1,2,3,4*,6
    *4 has typo. Need n≥2 and |Si|=n-1

    ThuFeb 23NothingIcepocalypse 2023: No class

    8TueFeb 28
  • The König-Egerváry Theorem
  • Perfect Matchings
  • CGT 1.7.3-1.7.41.7.3: 1,2,3(hard?)
    1.7.4: 1,2,4,5,6,7

    ThuMar 02Midterm Exam

    9TueMar 07Ramsey TheoryCGT 1.81.8.1: 1,3,4
    1.8.2: 1,2,4,5
    1.8.3: 2,3,4

    ThuMar 09Combinatorics: Some Essential ProblemsCGT 2-2.1HW 6 due
    2.1: 1,4,11,12,14

    10TueMar 14Binomial CoefficientsCGT 2.22.2: 1,2,4,6,7bd,8

    ThuMar 16Multinomial CoefficientsCGT 2.3HW 7 due
    2.3: 1,2,3,4,9ace,11
    Typo in 4: sum indices are missing "=n"

    Spring Break Week

    11TueMar 28The Pigeonhole PrincipleCGT 2.4HW 8 due
    2.4: 1,3,4,5,7,9,13

    ThuMar 30The Principle of Inclusion and ExclusionCGT 2.52.5: 2,4,6,8,12
    Error in 4: change 250 to 230

    12TueApr 04Generating FunctionsCGT 2.6-2.6.2HW 9 due
    2.6: 1,2
    2.6.1: 1,2,4
    2.6.2: 1,3,5,8

    ThuApr 06
  • Changing Money
  • Fibonacci Numbers
  • CGT 2.6.3-2.6.42.6.3: 1,3,9,10
    2.6.4: 1,2,5bd,10

    13TueApr 11
  • Recurrence Relations
  • Catalan Numbers
  • CGT 2.6.5-2.6.62.6.5:1,2ad,6,7
    2.6.6: 2,3,4

    ThuApr 13Counting ways to trianglalize n-gons

    14TueApr 18Pólya's Theory of Counting
  • Permutation Groups
  • Burnside Lemma
  • CGT 2.7-2.7.2HW 10 due
    2.7.1: 1,2,4,5,9
    2.7.2: 1,2,4

    ThuApr 20PartitionsCGT 2.8-2.8.12.8.1: 1,2,3,5,10

    15TueApr 25Stable Marriage CGT 2.9-2.9.1HW 11 due
    2.9: 1,4
    2.9.1: 1,3,4,8,7

    ThuApr 27Combinatorial Geometry
  • CGT 2.10-2.10.1
  • HW 12 due
    2.10.1: 1,2,6,9

    ExFriMay 05Final Exam
    12:30-2:20pm