Combinatorial Problems and Exercises (AMS Chelsea Publishing)

Front Matter
	Cover
	Title page
	Dedication
	Contents
	Preface to the second edition
	Preface
I. Problems
	§ 1. Basic enumeration
		1.1~1.2
		[Hint]1.1~1.7
		1.3~1.7
		[Ans]1.1~1.3
		[Ans]1.4~1.6
		[Ans]1.7
		1.8~1.14
		[Hint]1.8~1.17
		[Ans]1.8~1.9
		[Ans]1.10~1.11
		[Ans]1.12
		[Ans]1.13~1.14
		1.15~1.21
		[Hint]1.18~1.28
		[Ans]1.15
		[Ans]1.16
		[Ans]1.17~1.18
		[Ans]1.19
		[Ans]1.20~1.21
		1.22~1.28
		[Ans]1.22~1.23
		[Ans]1.24
		[Ans]1.25
		[Ans]1.26
		[Ans]1.27
		[Ans]1.28
		1.29~1.38
		[Hint]1.29~1.41
		[Ans]1.29
		[Ans]1.30
		[Ans]1.31~1.32
		[Ans]1.33
		[Ans]1.34
		[Ans]1.35~1.36
		[Ans]1.37~1.38
		1.39~1.42
		[Hint]1.42~2.8
		[Ans]1.39~1.40
		[Ans]1.41~1.42
		[Ans]1.43
		[Ans]1.44
		[Ans]1.45
	§ 2. The sieve
		2.1~2.2
		[Hint]2.1~2.8
		[Ans]2.1~2.2
		2.3~2.9
		[Hint]2.9~2.16
		[Ans]2.3
		[Ans]2.4~2.5
		[Ans]2.6~2.7
		[Ans]2.8~2.9
		2.10~2.15
		[Ans]2.10~2.11
		[Ans]2.12
		[Ans]2.13
		[Ans]2.14
		[Ans]2.15
		2.16~2.20
		[Hint]2.17~2.29
		[Ans]2.16
		[Ans]2.17
		[Ans]2.18
		[Ans]2.19~2.20
		2.21~2.28
		[Ans]2.21
		[Ans]2.22~2.23
		[Ans]2.24~2.25
		[Ans]2.26
		[Ans]2.27~2.29
		2.29~2.34
		[Hint]2.30~2.37
		[Ans]2.30
		[Ans]2.31~2.32
		[Ans]2.33
		[Ans]2.34~2.35
		2.35~2.37
		[Ans]2.36
		[Ans]2.37
	§ 3. Permutations
		3.1~3.5
		[Hint]3.1~3.8
		[Ans]3.1
		[Ans]3.2~3.4
		[Ans]3.5~3.6
		3.6~3.14
		[Hint]3.9~3.22
		[Ans]3.7
		[Ans]3.8
		[Ans]3.9
		[Ans]3.10
		[Ans]3.11~3.12
		[Ans]3.13~3.14
		3.15~3.22
		[Ans]3.15~3.16
		[Ans]3.17
		[Ans]3.18
		[Ans]3.19~3.21
		[Ans]3.22
		3.23~3.28
		[Hint]3.23~3.31
		[Ans]3.23
		[Ans]3.24~3.25
		[Ans]3.26~3.27
		[Ans]3.28
		3.29~3.31
		[Ans]3.29~3.31
	§ 4. Two classical enumeration problems in graph theory
		4.1~4.7
		[Hint]4.1~4.6
		[Ans]4.1
		[Ans]4.2~4.3
		[Ans]4.4~4.5
		[Ans]4.6
		[Ans]4.7
		4.8~4.12
		[Ans]4.8
		[Ans]4.9
		[Ans]4.10
		[Ans]4.11~4.12
		4.13~4.17
		[Hint]4.7~4.18
		[Ans]4.13
		[Ans]4.14
		[Ans]4.15~4.16
		[Ans]4.17
		4.18~4.22
		[Hint]4.19~4.28
		[Ans]4.18~4.19
		[Ans]4.20
		[Ans]4.21~4.24
		4.23~4.29
		[Hint]4.29~4.35
		[Ans]4.25
		[Ans]4.26~4.27
		[Ans]4.28~4.29
		4.30~4.33
		[Ans]4.30
		[Ans]4.31
		[Ans]4.32~4.33
		4.34~4.36
		[Hint]4.36
		[Ans]4.34~4.35
		[Ans]4.36
	§ 5. Parity and duality
		5.1
		[Hint]5.1~5.12
		[Ans]5.1
		5.2~5.12
		[Ans]5.2~5.3
		[Ans]5.4~5.5
		[Ans]5.6~5.10
		[Ans]5.11~5.13
		5.13~5.21
		[Hint]5.13~5.26
		[Ans]5.14~5.16
		[Ans]5.17
		[Ans]5.18
		[Ans]5.19~5.20
		[Ans]5.21~5.22
		5.22~5.31
		[Hint]5.27~5.38
		[Ans]5.23
		[Ans]5.24~5.27
		[Ans]5.28
		[Ans]5.29~5.31
		5.32~5.35
		[Ans]5.32
		[Ans]5.33
		[Ans]5.34~5.35
		5.36~5.38
		[Ans]5.36~5.37
		[Ans]5.38
	§ 6. Connectivity
		6.1~6.8
		[Hint]6.1~6.2
		[Hint]6.3~6.19
		[Ans]6.1~6.2
		[Ans]6.3~6.6
		[Ans]6.7~6.8
		6.9~6.17
		[Ans]6.9~6.11
		[Ans]6.12
		[Ans]6.13~6.17
		6.18~6.25
		[Hint]6.20~6.35
		[Ans]6.18~6.19
		[Ans]6.20~6.21
		[Ans]6.22~6.23
		[Ans]6.24~6.26
		6.26~6.32
		[Ans]6.27~6.29
		[Ans]6.30~6.32
		6.33~6.43
		[Hint]6.36~6.51
		[Ans]6.33
		[Ans]6.34~6.37
		[Ans]6.38~6.39
		[Ans]6.40~6.42
		[Ans]6.43~6.45
		6.44~6.52
		[Hint]6.52~6.64
		[Ans]6.46~6.48
		[Ans]6.49~6.51
		[Ans]6.52
		6.53~6.60
		[Ans]6.53~6.54
		[Ans]6.55~6.56
		[Ans]6.57~6.58
		[Ans]6.59~6.60
		6.61~6.72
		[Hint]6.65~6.75
		[Ans]6.61
		[Ans]6.62~6.64
		[Ans]6.65~6.66
		[Ans]6.67~6.68
		[Ans]6.69
		[Ans]6.70~6.72
		6.73~6.78
		[Hint]6.76~6.78
		[Ans]6.73~6.74
		[Ans]6.75
		[Ans]6.76
		[Ans]6.77
		[Ans]6.78
	§ 7. Factors of graphs
		7.1~7.5
		[Hint]7.1~7.8
		[Ans]7.1
		[Ans]7.2
		[Ans]7.3~7.4
		[Ans]7.5
		7.6~7.12
		[Hint]7.9~7.26
		[Ans]7.6
		[Ans]7.7~7.8
		[Ans]7.9
		[Ans]7.10~7.11
		[Ans]7.12~7.13
		7.13~7.19
		[Ans]7.14
		[Ans]7.15~7.16
		[Ans]7.17
		[Ans]7.18
		[Ans]7.19~7.20
		7.20~7.28
		[Hint]7.27~7.42
		[Ans]7.21
		[Ans]7.22~7.24
		[Ans]7.25~7.26
		[Ans]7.27
		[Ans]7.28
		7.29~7.33
		[Ans]7.29~7.30
		[Ans]7.31
		[Ans]7.32
		[Ans]7.33
		7.34~7.37
		[Ans]7.34
		[Ans]7.35
		[Ans]7.36
		[Ans]7.37
		[Hint]7.43~7.53
		7.38~7.48
		[Ans]7.38
		[Ans]7.39~7.41
		[Ans]7.42
		[Ans]7.43~7.45
		[Ans]7.46
		7.49~7.53
		[Ans]7.47~7.49
		[Ans]7.50~7.51
		[Ans]7.52~7.53
	§ 8. Independent sets of points
		8.1~8.8
		[Hint]8.1~8.8
		[Ans]8.1~8.4
		[Ans]8.5
		[Ans]8.6~8.8
		8.9~8.21
		[Hint]8.9~8.27
		[Ans]8.9~8.10
		[Ans]8.11~8.13
		[Ans]8.14~8.15
		[Ans]8.16~8.19
		8.22~8.27
		[Ans]8.20~8.22
		[Ans]8.23~8.25
		[Ans]8.26~8.27
	§ 9. Chromatic number
		9.1~9.9
		[Hint]9.1~9.12
		[Ans]9.1~9.2
		[Ans]9.3~9.6
		[Ans]9.7
		[Ans]9.8
		[Ans]9.9~9.10
		9.10~9.15
		[Hint]9.13~9.26
		[Ans]9.11~9.13
		[Ans]9.14
		[Ans]9.15~9.16
		9.16~9.19
		[Ans]9.17~9.18
		[Ans]9.19
		9.20~9.27
		[Hint]9.27~9.46
		[Ans]9.20~9.21
		[Ans]9.22~9.23
		[Ans]9.24~9.25
		[Ans]9.26
		[Ans]9.27
		9.28~9.36
		[Ans]9.28~9.29
		[Ans]9.30~9.31
		[Ans]9.32~9.34
		[Ans]9.35~9.36
		9.37~9.48
		[Hint]9.47~9.57
		[Ans]9.37~9.39
		[Ans]9.40~9.41
		[Ans]9.42~9.45
		[Ans]9.46~9.47
		[Ans]9.48~9.49
		9.49~9.57
		[Ans]9.50~9.51
		[Ans]9.52
		[Ans]9.53~9.54
		[Ans]9.55~9.57
	§10. Extremal problems for graphs
		10.1~10.4
		[Hint]10.1~10.2
		[Hint]10.3~10.16
		[Ans]10.1~10.3
		[Ans]10.4
		10.5~10.15
		[Ans]10.5
		[Ans]10.6~10.7
		[Ans]10.8~10.11
		[Ans]10.12~10.13
		[Ans]10.14~10.15
		10.16~10.24
		[Hint]10.17~10.28
		[Ans]10.16
		[Ans]10.17~10.18
		[Ans]10.19~10.20
		[Ans]10.21~10.22
		[Ans]10.23
		[Ans]10.24~10.25
		10.25~10.34
		[Hint]10.29~10.41
		[Ans]10.26~10.28
		[Ans]10.29
		[Ans]10.30
		[Ans]10.31~10.32
		[Ans]10.33~10.34
		10.35~10.41
		[Ans]10.35~10.36
		[Ans]10.37
		[Ans]10.38
		[Ans]10.39
		[Ans]10.40
		[Ans]10.41
		10.42~10.44
		[Hint]10.42~10.44
		[Ans]10.42~10.43
		[Ans]10.44
	§11. Spectra of graphs and random walks
		11.1~11.3
		[Hint]11.1~11.6
		[Ans]11.1
		[Ans]11.2
		[Ans]11.3~11.4
		11.4~11.12
		[Hint]11.7~11.21
		[Ans]11.5
		[Ans]11.6~11.7
		[Ans]11.8
		[Ans]11.9~11.10
		[Ans]11.11~11.12
		11.13~11.19
		[Ans]11.13~11.14
		[Ans]11.15~11.16
		[Ans]11.17
		[Ans]11.18~11.19
		11.20~11.28
		[Hint]11.22~11.35
		[Ans]11.20~11.21
		[Ans]11.22~11.23
		[Ans]11.24~11.25
		[Ans]11.26~11.27
		[Ans]11.28
		11.29~11.34
		[Ans]11.29
		[Ans]11.30~11.31
		[Ans]11.32
		[Ans]11.33
		[Ans]11.34~11.35
		11.35~11.44
		[Hint]11.36~11.45
		[Ans]11.36
		[Ans]11.37~11.38
		[Ans]11.39~11.40
		[Ans]11.41~11.42
		[Ans]11.43
		[Ans]11.44
		11.45~11.51
		[Hint]11.46~11.59
		[Ans]11.45
		[Ans]11.46~11.48
		[Ans]11.49~11.51
		11.52~11.56
		[Ans]11.52
		[Ans]11.53
		[Ans]11.54
		[Ans]11.55~11.56
		11.57~11.59
		[Ans]11.57
		[Ans]11.58
		[Ans]11.59
	§12. Automorphisms of graphs
		12.1~12.10
		[Hint]12.1~12.12
		[Ans]12.1
		[Ans]12.2
		[Ans]12.3~12.5
		[Ans]12.6
		[Ans]12.7
		[Ans]12.8~12.9
		[Ans]12.10~12.11
		12.11~12.20
		[Hint]12.13~12.25
		[Ans]12.12~12.13
		[Ans]12.14~12.15
		[Ans]12.16
		[Ans]12.17
		[Ans]12.18
		[Ans]12.19
		[Ans]12.20
		12.21~12.25
		[Ans]12.21
		[Ans]12.22~12.24
		[Ans]12.25
	§13. Hypergraphs
		13.1~13.8
		[Hint]13.1
		[Hint]13.2~13.13
		[Ans]13.1~13.2
		[Ans]13.3~13.4
		[Ans]13.5~13.6
		[Ans]13.7~13.8
		13.9~13.14
		[Hint]13.14~13.26
		[Ans]13.9
		[Ans]13.10
		[Ans]13.11~13.12
		[Ans]13.13~13.14
		13.15~13.23
		[Ans]13.15
		[Ans]13.16~13.17
		[Ans]13.18~13.19
		[Ans]13.20
		[Ans]13.21
		[Ans]13.22
		[Ans]13.23~13.24
		13.24~13.30
		[Hint]13.27~13.39
		[Ans]13.25~13.26
		[Ans]13.27~13.28
		[Ans]13.29
		[Ans]13.30~13.31
		13.31~13.37
		[Ans]13.32
		[Ans]13.33~13.35
		[Ans]13.36
		[Ans]13.37
		13.38~13.47
		[Hint]13.40~13.52
		[Ans]13.38~13.40
		[Ans]13.41~13.42
		[Ans]13.43~13.44
		[Ans]13.45
		[Ans]13.46
		[Ans]13.47
		[Ans]13.48~13.49
		13.48~13.55
		[Hint]13.53~13.57
		[Ans]13.50
		[Ans]13.51
		[Ans]13.52
		[Ans]13.53~13.54
		[Ans]13.55~13.56
		13.56~13.57
		[Ans]13.57
	§14. Ramsey Theory
		14.1~14.2
		[Hint]14.1~14.9
		[Ans]14.1
		[Ans]14.2
		14.3~14.10
		[Hint]14.10~14.12
		[Ans]14.3
		[Ans]14.4
		[Ans]14.5
		[Ans]14.6
		[Ans]14.7
		[Ans]14.8~14.10
		14.11~14.16
		[Hint]14.13~14.25
		[Ans]14.11~14.12
		[Ans]14.13~14.14
		[Ans]14.15~14.16
		14.17~14.21
		[Ans]14.17
		[Ans]14.18
		[Ans]14.19~14.20
		[Ans]14.21
		14.22~14.28
		[Hint]14.26~14.31
		[Ans]14.22
		[Ans]14.23
		[Ans]14.24
		[Ans]14.25~14.26
		[Ans]14.27
		[Ans]14.28
		14.29~14.31
		[Ans]14.29~14.30
		[Ans]14.31
	§15. Reconstruction
		15.1~15.5
		[Hint]15.1
		[Hint]15.2~15.10
		[Ans]15.1
		[Ans]15.2
		[Ans]15.3
		[Ans]15.4~15.5
		15.6~15.11
		[Hint]15.11~15.21
		[Ans]15.6
		[Ans]15.7
		[Ans]15.8
		[Ans]15.9
		[Ans]15.10~15.11
		15.12~15.16
		[Ans]15.12
		[Ans]15.13
		[Ans]15.14~15.15
		[Ans]15.16
		15.17~15.22
		[Hint]15.22
		[Ans]15.17
		[Ans]15.18~15.19
		[Ans]15.20
		[Ans]15.21~15.22
II. Hints
	§ 1
	§ 2
	§ 3
	§ 4
	§ 5
	§ 6
	§ 7
	§ 8
	§ 9
	§10
	§11
	§12
	§13
	§14
	§15
III. Solutions
	§ 1. Basic enumeration
	§ 2. The sieve
	§ 3. Permutations
	§ 4. Two classical enumeration problems in graph theory
	§ 5. Parity and duality
	§ 6. Connectivity
	§ 7. Factors of graphs
	§ 8. Independent sets of points
	§ 9. Chromatic number
	§10. Extremal problems for graphs
	§11. Spectra of graphs
	§12. Automorphisms of graphs
	§13. Hypergraphs
	§14. Ramsey Theory
	§15. Reconstruction
Back Matter
	Dictionary of the combinatorial phrases and concepts used
	Notation
	Index of the abbreviations of textbooks and monographs
	Subject index
	Author index
	Errata
	Back Cover