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  2. Linear inequality - Wikipedia

    en.wikipedia.org/wiki/Linear_inequality

    Two-dimensional linear inequalities are expressions in two variables of the form: + < +, where the inequalities may either be strict or not. The solution set of such an inequality can be graphically represented by a half-plane (all the points on one "side" of a fixed line) in the Euclidean plane. [2]

  3. Inequality (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Inequality_(mathematics)

    Later in 1734, ≦ and ≧, known as "less than (greater-than) over equal to" or "less than (greater than) or equal to with double horizontal bars", first appeared in Pierre Bouguer's work . [3] After that, mathematicians simplified Bouguer's symbol to "less than (greater than) or equal to with one horizontal bar" (≤), or "less than (greater ...

  4. Connectivity (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Connectivity_(graph_theory)

    The edge-connectivity for a graph with at least 2 vertices is less than or equal to the minimum degree of the graph because removing all the edges that are incident to a vertex of minimum degree will disconnect that vertex from the rest of the graph. [1] For a vertex-transitive graph of degree d, we have: 2(d + 1)/3 ≤ κ(G) ≤ λ(G) = d. [11]

  5. Relation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Relation_(mathematics)

    Greater than; Greater than or equal to; Less than; Less than or equal to; Divides (evenly) Subset of; Equivalence relations: Equality; Parallel with (for affine spaces) Is in bijection with; Isomorphic; Tolerance relation, a reflexive and symmetric relation: Dependency relation, a finite tolerance relation; Independency relation, the complement ...

  6. Floor and ceiling functions - Wikipedia

    en.wikipedia.org/wiki/Floor_and_ceiling_functions

    In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]

  7. Max-flow min-cut theorem - Wikipedia

    en.wikipedia.org/wiki/Max-flow_min-cut_theorem

    Also, since any flow in the network is always less than or equal to capacity of every cut possible in a network, the above described cut is also the min-cut which obtains the max-flow. A corollary from this proof is that the maximum flow through any set of edges in a cut of a graph is equal to the minimum capacity of all previous cuts.

  8. Brooks' theorem - Wikipedia

    en.wikipedia.org/wiki/Brooks'_theorem

    If the graph has a vertex v with degree less than Δ, then a greedy coloring algorithm that colors vertices farther from v before closer ones uses at most Δ colors. This is because at the time that each vertex other than v is colored, at least one of its neighbors (the one on a shortest path to v ) is uncolored, so it has fewer than Δ colored ...

  9. Bipartite graph - Wikipedia

    en.wikipedia.org/wiki/Bipartite_graph

    A graph is bipartite if and only if it is 2-colorable, (i.e. its chromatic number is less than or equal to 2). [3] A graph is bipartite if and only if every edge belongs to an odd number of bonds, minimal subsets of edges whose removal increases the number of components of the graph. [16]