Linearly embedded graphs in 3–space with homotopically free exteriors

Linearly $\chi$-Bounding $(P_6,C_4)$-Free Graphs

Given two graphs H1 and H2, a graph G is (H1,H2)-free if it contains no subgraph isomorphic to H1 or H2. Let Pt and Cs be the path on t vertices and the cycle on s vertices, respectively. In this paper we show that for any (P6, C4)-free graph G it holds that χ(G) ≤ 3 2 ω(G), where χ(G) and ω(G) are the chromatic number and clique number of G, respectively. Our bound is attained by several graph...

Graphs with Linearly Bounded Ramsey Numbers

$C_4$-free zero-divisor graphs

‎In this paper we give a characterization for all commutative‎ ‎rings with $1$ whose zero-divisor graphs are $C_4$-free.‎

Embedding Graphs into Embedded Graphs

A drawing of a graph G in the plane is weakly simple if it can be turned into an embedding by an arbitrarily small perturbation. We show that testing, whether a straight-line drawing of a planar graph G in the plane is weakly simple, can be carried out in polynomial time, if a desired embedding of G belongs to a fixed isotopy class. In other words, we show that c-planarity with pipes is tractab...

Drawing Simultaneously Embedded Graphs with Few Bends