Chapter 3: Connectivity and Paths Flashcards
(50 cards)
1
Q
Adjacency Matrix Walk Counting
A
2
Q
Vertex/Edge Relationship with Connected Components
A
3
Q
Connected Graph on n vertices has how many edges?
A
4
Q
Euler’s Theorem (Eulerian Graph)
A
5
Q
All degrees even means what for maximal trails?
A
6
Q
Semi-Eulerian Condition
A
7
Q
Fleury’s Algorithm
A
8
Q
Hamiltonian Cycle Relationship with connected components
A
9
Q
Hamiltonian and Bipartite implies
A
10
Q
Dirac’s Theorem
A
11
Q
Ore’s Theorem
A
12
Q
Tree Leaf Facts
A
13
Q
Edges in a cycle are not…
A
14
Q
Characterisation of Trees with n vertices
A
15
Q
Tree/Path Condition
A
16
Q
Tree More Facts
A
17
Q
Prüfer Code Facts
A
18
Q
Cayley’s Theorem, 1889
A
19
Q
Matching/Augmenting Path Relationship
A
20
Q
Berge, 1957
A
21
Q
Hall’s Theorem
A
22
Q
k-regular, Bipartite implies
A
23
Q
Corollary 1.12 (Bipartite, Neighbourhood, Cardinality)
A
24
Q
1-Factor Facts
A
25
Tutte 1947
26
Bipartite perfect matching decomposition condition
27
Which complete graphs are 1-factorable?
28
2-Factor Facts
29
Regular graph of positive even degree has…
30
Which Complete Graphs are 2-Factorable?
31
Vizing’s Theorem
32
Bipartite Graphs and Delta(G) regular graphs
33
Bipartite Graph Edge Chromatic Number
34
Edge Chromatic Number of Complete Graph
35
Jordan Curve Theorem
36
Boundary Edge Condition
37
Handshaking Lemma for Planar Graphs
38
Euler’s Formula for Planar Graphs
39
2-connected Planar Graph
40
Planar Graph Edge Bound
41
Connected Planar Graph Degree Condition
42
Kuratowski’s Theorem
43
Four Colour Theorem
44
Chromatic Number Bound
45
Brooke’s Theorem
46
Chromatic Polynomial of Connected Components
47
Deletion/Contraction Lemma
48
Chromatic Polynomial Characteristics
49
Chromatic Polynomial of Tree
50
Chromatic Polynomial of Cyclic Graph
