Problem Garden

The problems submitted by GRWC participants in their applications are used to start research collaborations at the workshop. After the collaborations have had time to start and build initial results, all problem statements of the participants are made public in this Problem Garden.

Notes:

A problem with a * at the end corresponds to a paper generated by GRWC group, as listed on our Research Papers page.
A problem with a ** at the end corresponds to a paper from a GRWC group that is being actively worked. Please contact Combinatorics.Workshop@gmail.com before starting work on these problems.

2019 GRWC held in Lawrence, KS

Computing Tutte polynomials of hyperplane arrangements
Flexibility of planar graphs *
G-parking functions, spanning trees, and the Tutte polynomial *
Graded posets and Whitney duals
Problem on polynomial poset
Coloring problems on cubic graphs
The number of edges of C_4-free graphs
On a conjecture of Bezrukavnikov
Problems related to the Heisenberg product
Antimagic orientations of graphs *
P-matchings in graphs
A canonical construction of tessellated 3-dimensional pseudomanifold
Hadamard diagonalizable graphs *
Density of cospectral graphs
P_3-factors in 3-regular, 3-connected graphs
Steiner systems, designs and (strongly regular) graphs
Permutations which are "far" from avoiding other permutations
DNA graph characterization for DNA sequencing
Infinite odd cycle saturation games
Erdos-Szekeres on-line variation
Swapping numbers of graphs
Extremal problems related to Erdos-Szekeres

Maker-Breaker games on vertex sets of random graphs
Lattice polytopes arising from Schur polynomials *
Arithmetical structures of integer matrices
Problems related to the Pak-Stanley labeling
Equitable edge-colored G-designs and partial G-designs
Problems related to forbidding rainbow cycles
Tuza's conjecture
Strengthenings of Ryser's conjecture
Throttling cop-win graphs
Discrepancy in random hypergraphs *
On the number of disjoint cycles of specific lengths in tournaments
Problems related to Schubert polynomials
Extending interlace polynomial results to Eulerian graphs
Maximizing the number of λ-colorings among (n,n^2/4)-graphs
The game of plates and olives
The order polytope of Young's lattice
Graphs with subgraphs of large girth and chromatic numbers
Random adjacency matrices
Graph Nim on weighted trees
Maker-Breaker k-AP game
Special cases of the Frankl-Furedi conjecture
Throttling for cops and robbers on toroidal chess graphs
Data loss in two-mode networks

2018 GRWC held in Ames, IA

Higher powers of higher nerves
Fibonomial identities
Preferential attachment with 2D choice
Edge decompositions of complete bipartite graphs**
List coloring square graphs
Minimum rank for matrices of double branched graphs
Piercing numbers in approval voting
Exploring coefficients of minimal polynomials
The Nikiforov technique
Packing coloring and T-coloring of subcubic graphs
A generalization of Riordan arrays
Tetrahedral and trapezoidal posets
Edge maximal embeddings of graphs into surfaces
Hadamard-like matrices
Strategies in the game of Cops and Robbers*
Graph information ratios
Inducibility of cycles
Partitionability Problems
Quasirandom permutation forcing sets
Non-negativity of Elser's invariant*
Invariants of quotients of numerical semigroups*
Triangle-edge decompositions of graphs**
Graphs with circular coloring less than 3
Chip firing with hypergraphs

Topology of matching complexes
Power domination in reconfigurable graphs
Cyclic sieving of matchings
Problems related to the Erdos-Gyarfas Conjecture
Bounds on generalised radius for special classes of graphs
Constructions of Cospectral Distance Laplacian Graphs*
On the Hall ratio *
Saturation in the hypercube
Colored Eulerian polynomials and unimodality
Permutation packing density
Minkowski sum of all diagonals of hypercubes
The exponents of k-primitive digraphs
Problems related to parking functions*
Maxmizing H-colorings of graphs with minimum degree
Some problems related to sets of line segments *
Matching sequencibility on graphs
Minimally non-linear patterns
Graceful labeling problems*
Permutation class preimages under stack-sorting algorithm*
Face numbers of self-dual 4-dimensional polytopes
The inertia bound for Hermitian matrices
Comparing Ramsey numbers of ordered graphs*
Critical ideals of graphs and applications**

On-Line Size Ramsey Numbers variant 1
On-Line Size Ramsey Numbers variant 2
Random Threshold Hypergraphs
d-distance Vertex-distinguishing Index
Detecting Sumsets in Groups
The Turnpike Problem (Distance Multisets)
Partitioning into Locally Irregular Subgraphs
Two Graph Coloring Problems
Hadwiger Number
The Regular and Misere Form of Edge-NIM on General Graphs
The Saturation Number of a Union of Three Cliques of Different Order
The Earth-Moon Problem
Probabilistic Consequences of Polynomial Recurrences
Knot Mosaics and the Mosaic Number
A Dimension-Reduction Analogue for Integer Programming
Fractional Ramsey Theory
Subtractive Magic Total Labeling
An Extension of the Longest Increasing Path Problem
Families of Partitions with Restricted Intersections
The Enhanced Principal Permanent Rank Characteristic Sequence
Colored Paths in Tournaments

2014 GRWC held in Denver, CO

Antimagic-type Labelings*
A Problem in Incidence Geometry
Bootstrap Percolation on the Hexagonal Lattice**
Choosability of Graph Powers
Choosing Committees in Agreeable Societies
Color-Blind Index of Graphs*
Connectivity of Randomly-Oriented Graphs*
Counting Maximal Chains in Set Families
Covering Colored Graphs with Colored Cycles
Extremal Problems using the Absorbing Method
Forbidden Induced Posets
Gray Codes for Acyclic Orientations of Graphs

Gyarfas' Forbidden Subgraph Conjecture
Halin Graphs
Hamburger Moment Problem
Hyperfocused Arcs**
Increasing Paths in Edge-Ordered Graphs*
Inverse Principal Perrank Sequences*
Minimum Rank Problems**
PSD Minimum Rank of Hamming Graphs
Potential Ramsey Numbers
Pseudo-Winners for Digraphs
Reconstructing Trees from Symmetric Chromatic Polynomials
Strong Chromatic Index*
Turan Numbers for Small Bipartite Graphs

Problem Garden

2021 GRWC held virtually

2019 GRWC held in Lawrence, KS

2018 GRWC held in Ames, IA

2017 GRWC held in Denver, CO

2016 GRWC held in Laramie, WY

2015 GRWC held in Ames, IA

2014 GRWC held in Denver, CO