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Distribution and upper bound of mimic numbers ★★
Author(s): Bhattacharyya
Let the notation denote '' divides ''. The mimic function in number theory is defined as follows [1].
By using this definition of mimic function, the mimic number of any non-prime integer is defined as follows [1].
Given these two definitions and a positive integer , find the distribution of mimic numbers of those numbers divisible by .
Again, find whether there is an upper bound of mimic numbers for a set of numbers divisible by any fixed positive integer .
Keywords: Divisibility; mimic function; mimic number
Coloring random subgraphs ★★
Author(s): Bukh
If is a graph and , we let denote a subgraph of where each edge of appears in with independently with probability .
Keywords: coloring; random graph
Are vertex minor closed classes chi-bounded? ★★
Author(s): Geelen
Keywords: chi-bounded; circle graph; coloring; vertex minor
Graphs with a forbidden induced tree are chi-bounded ★★★
Author(s): Gyarfas
Say that a family of graphs is -bounded if there exists a function so that every satisfies .
Keywords: chi-bounded; coloring; excluded subgraph; tree
Asymptotic Distribution of Form of Polyhedra ★★
Author(s): Rüdinger
Keywords: polyhedral graphs, distribution
Domination in plane triangulations ★★
Keywords: coloring; domination; multigrid; planar graph; triangulation
Erdös-Szekeres conjecture ★★★
Keywords: combinatorial geometry; Convex Polygons; ramsey theory
Inequality of the means ★★★
Author(s):
Keywords: arithmetic mean; geometric mean; Inequality; packing
P vs. PSPACE ★★★
Author(s): Folklore
Keywords: P; PSPACE; separation; unconditional
Sums of independent random variables with unbounded variance ★★
Author(s): Feige
Keywords: Inequality; Probability Theory; randomness in TCS
Grunbaum's Conjecture ★★★
Author(s): Grunbaum
Refuting random 3SAT-instances on $O(n)$ clauses (weak form) ★★★
Author(s): Feige
Given is a 3SAT (3CNF) formula on variables, for some , and clauses drawn uniformly at random from the set of formulas on variables. Return with probability at least 0.5 (over the instances) that is typical without returning typical for any instance with at least simultaneously satisfiable clauses.
Keywords: NP; randomness in TCS; satisfiability
Does the chromatic symmetric function distinguish between trees? ★★
Author(s): Stanley
Keywords: chromatic polynomial; symmetric function; tree
Shannon capacity of the seven-cycle ★★★
Author(s):
Keywords:
Frobenius number of four or more integers ★★
Author(s):
Keywords:
Magic square of squares ★★
Author(s): LaBar
Keywords:
Inverse Galois Problem ★★★★
Author(s): Hilbert
Keywords:
Seymour's r-graph conjecture ★★★
Author(s): Seymour
An -graph is an -regular graph with the property that for every with odd size.
Keywords: edge-coloring; r-graph
Edge list coloring conjecture ★★★
Author(s):
Keywords: