Waterloo Research: Recent submissions
Now showing items 2140 of 2173

Sandwich and probe problems for excluding paths
(Elsevier, 20181231)Let Pk denote an induced path on k vertices. For k ≥ 5, we show that the Pkfree sandwich problem, partitioned probe problem, and unpartitioned probe problem are NPcomplete. For k ≤ 4, it is known that the Pkfree sandwich ... 
Minimal induced subgraphs of two classes of 2connected nonHamiltonian graphs
(Elsevier, 202207)In 1981, Duffus, Gould, and Jacobson showed that every connected graph either has a Hamiltonian path, or contains a claw (K1,3) or a net (a fixed sixvertex graph) as an induced subgraph. This implies that subject to being ... 
On symmetric intersecting families of vectors
(Cambridge University Press, 202111)A family of vectors in [k]n is said to be intersecting if any two of its elements agree on at least one coordinate. We prove, for fixed k ≥ 3, that the size of any intersecting subfamily of [k]n invariant under a transitive ... 
Modular relations of the Tutte symmetric function
(Elsevier, 202204)For a graph G, its Tutte symmetric function XBG generalizes both the Tutte polynomial TG and the chromatic symmetric function XG. We may also consider XB as a map from the textended Hopf algebra G[t] of labelled graphs ... 
Finding Large HColorable Subgraphs in Hereditary Graph Classes
(Society for Industrial and Applied Mathematics, 20211014)We study the Max Partial HColoring problem: given a graph G, find the largest induced subgraph of G that admits a homomorphism into H, where H is a fixed pattern graph without loops. Note that when H is a complete graph ... 
A Complete Multipartite Basis for the Chromatic Symmetric Function
(Society for Industrial and Applied Mathematics, 20211115)In the vector space of symmetric functions, the elements of the basis of elementary symmetric functions are (up to a factor) the chromatic symmetric functions of disjoint unions of cliques. We consider their graph complements, ... 
Pure Pairs VI. Excluding an Ordered Tree.
(Society for Industrial and Applied Mathematics Journal on Discrete Mathematics, 202201)A pure pair in a graph G is a pair (Z1,Z2) of disjoint sets of vertices such that either every vertex in Z1 is adjacent to every vertex in Z2, or there are no edges between Z1 and Z2. With Maria Chudnovsky, we recently ... 
The Pivot of Athwartedness: Roy Kiyooka's "Pacific Windows"
(Guernica, 2020)Published as a full issue of The Capilano Review in August 1990, Roy Kiyooka’s “Pacific Windows” exists on the periphery of Kiyooka’s canon. Despite the various ways in which this text could be considered the culmination ... 
Plethysms of Chromatic and Tutte Symmetric Functions
(The Electronic Journal of Combinatorics, 2022)Plethysm is a fundamental operation in symmetric function theory, derived directly from its connection with representation theory. However, it does not admit a simple combinatorial interpretation, and finding coefficients ... 
Concatenating Bipartite Graphs
(The Electronic Journal of Combinatorics, 2022)Let x, y E (0, 1], and let A, B, C be disjoint nonempty stable subsets of a graph G, where every vertex in A has at least x B neighbors in B, and every vertex in B has at least yC neighbors in C, and there are no edges ... 
Fourcoloring P6free graphs
(Association for Computing Machinery, 2019)In this paper we present a polynomial time algorithm for the 4COLORING PROBLEM and the 4PRECOLORING EXTENSION problem restricted to the class of graphs with no induced sixvertex path, thus proving a conjecture of Huang. ... 
Approximately Coloring Graphs Without Long Induced Paths
(Springer Nature, 2017)It is an open problem whether the 3coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on t vertices, for fixed t. We propose an algorithm that, given a 3colorable ... 
Polynomial bounds for chromatic number II: Excluding a starforest
(Wiley, 202210)The Gyárfás–Sumner conjecture says that for every forest H, there is a function fH such that if G is Hfree then x(G) ≤ fH(w(G)) (where x,w are the chromatic number and the clique number of G). Louis Esperet conjectured ... 
Polynomial bounds for chromatic number. III. Excluding a double star
(Wiley, 202210)A “double star” is a tree with two internal vertices. It is known that the GyárfásSumner conjecture holds for double stars, that is, for every double star H, there is a function fH such that if G does not contain H as ... 
Piercing axisparallel boxes
(The Electronic Journal of Combinatorics, 2018)Let F be a finite family of axisparallel boxes in Rd such that F contains no k + 1 pairwise disjoint boxes. We prove that if F contains a subfamily M of k pairwise disjoint boxes with the property that for every F E F ... 
Even pairs and prism corners in squarefree Berge graphs
(Elsevier, 201807)Let G be a Berge graph such that no induced subgraph is a 4cycle or a linegraph of a bipartite subdivision of K4. We show that every such graph G either is a complete graph or has an even pair. 
Complexity of CkColoring in Hereditary Classes of Graphs
(Schloss DagstuhlLeibnizZentrum fuer Informatik, 2019)For a graph F, a graph G is Ffree if it does not contain an induced subgraph isomorphic to F. For two graphs G and H, an Hcoloring of G is a mapping f : V (G) > V (H) such that for every edge uv E(G) it holds that ... 
Hcolouring Ptfree graphs in subexponential time
(Elsevier, 20190831)A graph is called Ptfree if it does not contain the path on t vertices as an induced subgraph. Let H be a multigraph with the property that any two distinct vertices share at most one common neighbour. We show that the ... 
Trianglefree graphs that do not contain an induced subdivision of K4 are 3colorable
(Wiley, 201910)We show that trianglefree graphs that do not contain an induced subgraph isomorphic to a subdivision of K4 are 3colorable. This proves a conjecture of Trotignon and Vušković. 
Induced subgraphs of graphs with large chromatic number. VIII. Long odd holes
(Elsevier, 202001)We prove a conjecture of András Gyárfás, that for all k, l, every graph with clique number at most κ and sufficiently large chromatic number has an odd hole of length at least ℓ.