Browsing University of Waterloo by Author "Qu, Zishen"
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Combinatorial Generalizations of Sieve Methods and Characterizing Hamiltonicity via Induced Subgraphs
Qu, Zishen (University of Waterloo, 2022-08-17)A sieve method is in effect an application of the inclusion-exclusion counting principle, and the estimation methods to avoid computing the explicit formula. Sieve methods have been used in number theory for over a hundred ... -
Minimal induced subgraphs of the class of 2-connected non-Hamiltonian wheel-free graphs
Chaniotis, Aristotelis; Qu, Zishen; Spirkl, Sophie (Elsevier ScienceDirect, 2022-12-29)Given a graph G and a graph property P we say that G is minimal with respect to P if no proper induced subgraph of G has the property P. An HC-obstruction is a minimal 2-connected non-Hamiltonian graph. Given a graph H, a ... -
Minimal induced subgraphs of two classes of 2-connected non-Hamiltonian graphs
Cheriyan, Joseph; Hajebi, Sepehr; Qu, Zishen; Spirkl, Sophie (Elsevier, 2022-07)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 six-vertex graph) as an induced subgraph. This implies that subject to being ...