Let G be a connected graph with V (G) ≥ 2, and assume that G has no cycle of even length Prove that every block of G is either an edge or an odd cycle
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[PDF] 2-Connected Graphs Definition 1 A graph is connected if for any two
Theorem 1 (Whitney, 1927) A connected graph G with at least three vertices is 2- connected iff for every two vertices x, y ∈ V (G), there is a cycle containing both
[PDF] A characterisation of some 2-connected graphs and a - CORE
A simple characterisation of cycles and complete graphs highlights their significance in Brooks' theorem connected graph in which each vertex has degree 2
[PDF] Hamilton Cycles in Regular 2-Connected Graphs - CORE
Every 2-connected, k-regular graph on at most 3k vertices This result is best to investigate the cases n = 3k - 1 and n = 3k in which R contains no isolated
Hamilton Cycles in Regular 2-Connected Graphs - ScienceDirectcom
Every 2-connected, k-regular graph on at most 3k vertices This result is best to investigate the cases n = 3k - 1 and n = 3k in which R contains no isolated
[PDF] Homework 8 Solutions
Let G be a connected graph with V (G) ≥ 2, and assume that G has no cycle of even length Prove that every block of G is either an edge or an odd cycle
[PDF] MATH 154 Homework 2 Solutions Due October 19, 2012 - UCSD Math
19 oct 2012 · every closed odd walk with no more than n repeated vertices contains an (2) Prove that every 2-connected graph contains at least one cycle
[PDF] Solutions to problem sheet 6
2 (n − 1) You may use the following fact without proof: For each k ≥ 2, each 2- connected graph with minimum degree k contains a cycle of length at least 2k or
[PDF] Graph Theory - MIT OpenCourseWare
vertex has degree 2 Theorem 7: A graph is 2-regular if and only if all its connected components are cycles Proof: One direction of the theorem is trivial – a graph
[PDF] Math776: Graph Theory (I) Fall, 2017 Homework 4 solutions
Then, it follows from symmetry that X meets every component of G−X 2 [page 83, #10 ] Let e be an edge in a 3-connected graph G = K4 Show that either Let C be a largest cycle in G First, as δ(G) ≥ κ(G) ≥ k and G has a cycle, C ≥ k +
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