Algorithms Analysis Practice Test 2025 – All-in-One Mastery Guide to Exam Success

A bipartite graph is defined as a graph whose vertices can be divided into two distinct sets such that no two vertices within the same set are adjacent. This structure leads to certain properties relating to cycles within the graph. One of the fundamental characteristics of bipartite graphs is that all cycles must be of even length. This occurs because, when traversing a cycle within the graph, you must alternate between the two sets of vertices. Starting from any vertex in one set, as you move through edges to reach another vertex in the opposite set and return to your starting vertex, you move through an even number of edges, ensuring the cycle length is even.

The other characteristics presented are not true for all bipartite graphs. For instance, being constrained to cycles of even length does not imply that all vertices must have the same degree, which can vary significantly. Additionally, while bipartite graphs can be represented with directed edges, they usually focus on undirected connections. Lastly, a bipartite graph does not restrict connectivity such that every vertex is only connected to one other vertex; rather, vertices in one set can be connected to multiple vertices in the other set, allowing for a more complex structure. Thus, the defining property regarding cycle lengths solid