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Undergraduate
By
diego
on June 27, 2012 | Updated Dec. 6, 2017
Unmatchable edges of bipartite graphs
Prove that the following algorithm finds the unmatchable edges of a bipartite graph \(G\) (edges that aren't in any perfect matching): find a perfect matching in \(G\), orient the unmatched edges from…
Mathematics
Graph Theory
bipartite graph
matching
0
High School
By
True IITJEE
on Jan. 7, 2017 | Updated Jan. 3, 2018
JEE Advanced 2016 Paper 1 Mathematics Question 41
The least value of \(\alpha \in \mathbb{R}\) for which \(4\alpha {x}^2 + \frac{1}{x} \geq 1\), for all \(x > 0\), is
Mathematics
Calculus
differentiation
inequality
jee
jee 2016
jee advanced
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Graduate
By
Shiva Kintali
on Sept. 11, 2012 | Updated Dec. 6, 2017
Vertex cover in bipartite graphs
The Vertex Cover of a graph \(G(V,E)\) is a set of vertices \(S \subseteq V\) such that each edge of the graph is incident to at least one vertex of the set \(S\). Minimum cost vertex cover : Given a…
Mathematics
Optimization
Graph Theory
Linear Programming
bipartite graph
vertex cover
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Undergraduate
By
Shiva Kintali
on July 30, 2012 | Updated Dec. 6, 2017
k-regular bipartite graphs are 2-connected
Prove that every connected \(k\)-regular bipartite graph on at least three vertices is 2-connected.
Mathematics
Graph Theory
bipartite graph
connectivity
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Undergraduate
By
Shiva Kintali
on May 19, 2013 | Updated Dec. 6, 2017
Regular bipartite super-graph
Let \(G\) be a simple bipartite graph where each side of the bi-partition has size \(n\). The maximum degree of \(G\) is \(\Delta \le n/10\). Show that there exists a \(2 \Delta\)-regular simple bip…
Computer Science
Mathematics
Algorithms
Graph Theory
bipartite graph
graph algorithms
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Graduate
By
Shiva Kintali
on Sept. 23, 2012 | Updated Dec. 6, 2017
Characterizing factor-critical graphs
A graph \(G\) is said to be factor-critical if \(G-v\) has perfect matching for every \(v \in V(G)\). Prove that no bipartite is factor-critical. Show that \(G\) is factor-critical if and only if …
Mathematics
Graph Theory
bipartite graph
matching
0
High School
By
True IITJEE
on Jan. 16, 2017 | Updated Jan. 3, 2018
JEE Advanced 2016 Paper 1 Mathematics Question 46
A solution curve of the differential equation \(\displaystyle(x^2 + xy + 4x + 2y + 4) \frac{dy}{dx} - y^2 = 0, \ \ \ x > 0\), passes through the point \((1,3)\). Then the solution curve
Mathematics
Calculus
differentiation
jee
jee 2016
jee advanced
jee mathematics
0
High School
By
True IITJEE
on Jan. 16, 2017 | Updated Jan. 3, 2018
JEE Advanced 2016 Paper 1 Mathematics Question 43
Let \(f : (0, \infty) \rightarrow \mathbb{R}\) be a differentiable function such that \(f' (x) = 2 - \frac{f(x)}{x}\) for all \(x \in (0 , \infty)\) and \(f(1) \neq 1\). Then
Mathematics
Calculus
differentiation
jee
jee 2016
jee advanced
jee mathematics
limits
0
Undergraduate
By
Shiva Kintali
on May 21, 2013 | Updated Dec. 6, 2017
Covering complete graph with bipartite graphs
The union of graphs \(G_1, \dots, G_k\), written \(G_1 \cup \dots \cup G_k\), is the graph with vertex set \(V(G_1) \cup \dots \cup V(G_k)\) and edge set \(E(G_1) \cup \dots \cup E(G_k)\). Prove tha…
Mathematics
Graph Theory
bipartite graph
graph union
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High School
By
True IITJEE
on Jan. 17, 2017 | Updated Jan. 3, 2018
JEE Advanced 2016 Paper 1 Mathematics Question 52
The total number of distinct \(x \in [0,1]\) for which \(\displaystyle\int_0^x \frac{t^2}{1+t^4} dt = 2x - 1\) is
Mathematics
Calculus
differentiation
integration
jee
jee 2016
jee advanced
jee mathematics
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