Preregistration deadline: April 11

- 9:00-9:30 Sang-il Oum (엄상일), KAIST : Rank-width and well-quasi-ordering of skew-symmetric or symmetric matrices
- 9:30-10:00 Sejeong Bang (방세정), Yeungnam University : Geometric distance-regular graphs with smallest eigenvalue -3
- 10:00-10:10 Break
- 10:10-11:40 Mark H. Siggers, Kyungpook National University : The H-colouring Dichotomy through a projective property
- 10:10-10:40 Tommy R. Jensen, Kyungpook National University : On second Hamilton circuits in cubic graphs
- 11:10-11:40 Jack Koolen, POSTECH : Recent progress of distance-regular graphs

Organized by Seog-Jin Kim (Konkuk University) and Sang-il Oum (KAIST).

At 14:00-14:40, there will be an invited talk by Xuding Zhu, *Thue choice number of graphs*.

Department of Mathematical Sciences, KAIST

_{1}, M

_{2}, … over a fixed finite field must have a pair M

_{i}, M

_{j}(i<j) such that that M

_{i}is isomorphic to a principal submatrix of the Schur complement of a nonsingular principal submatrix in M

_{j}, if those matrices have bounded rank-width. This generalizes three theorems on well-quasi-ordering of graphs or matroids admitting good tree-like decompositions; (1) Robertson and Seymour’s theorem for graphs of bounded tree-width, (2) Geelen, Gerards, and Whittle’s theorem for matroids representable over a fixed finite field having bounded branch-width, and (3) Oum’s theorem for graphs of bounded rank-width with respect to pivot-minors.

Department of Mathematics, Yeungnam University

_{1}+1)/3}<k<4a

_{1}+10−6c

_{2}. To prove this result, we first show by considering non-existence of 4-claws that any non-complete distance-regular graph satisfying max{3,8(a

_{1}+1)/3}<k<4a

_{1}+10−6c

_{2}is a geometric distance-regular graph with smallest eigenvalue −3. Moreover, we classify the geometric distance-regular graphs with smallest eigenvalue −3. As an application, 7 feasible intersection arrays are ruled out.

Department of Mathematics, Kyungpook National University

In this talk we present a short new proof of this result, recently published, using a new projective property defined for homomorphisms of powers of a graph G onto a graph H.

Department of Mathematics, Kyungpook National University

Department of Mathematics, POSTECH

(Invited lecture at 2PM)

Institute of Mathematics, Zhejiang Normal University, Jinhua, China

Thue-choice number of a graph G is the list version of its Thue-chromatic number, which is the minimum integer k such that if each vertex of G is given k-permissible colours, then there is a Thue-colouring of G using a permissible colour for each vertex. This talk will survey some research related to Thue Theorem and will show that Thue-choice number of paths is at most 4 and Thue choice number of trees are unbounded.