This book collects the extended abstracts of the accepted contributions to EuroComb21. A similar book is published at every edition of EuroComb (every two years since 2001) collecting the most recent advances in combinatorics, graph theory, and related areas. It has a wide audience in the areas, and the papers are used and referenced broadly.

Inhalt
Size of local finite field Kakeya sets.- Coloring of Graphs Avoiding Bicolored Paths of a Fixed Length.- Nested cycles with no geometric crossings.- Cut vertices in random planar graphs.- Extremal density for sparse minors and subdivisions.- Enumerating descents on quasi-Stirling permutations and plane trees.- Hamiltonicity of randomly perturbed graphs.- The largest hole in sparse random graphs.- On 13-Crossing-Critical Graphs with Arbitrarily Large Degrees.- Local convergence of random planar graphs.- Some results on the Laplacian spectra of token graphs.- On the Number of Compositions of Two Polycubes.- Halin's end degree conjecture.- Coloring Circle Arrangements: New 4-Chromatic Planar Graphs.- A Short Proof of EulerPoincaré Formula.- Approximate MDS Property of Linear Codes.- A SAT attack on higher dimensional Erd\H{o}s--Szekeres numbers.- Improved bounds on the cop number of a graph drawn on a surface.- Stability of Berge-hypergraphs]{Stability of extremal connected hypergraphs avoiding Berge-paths, (extended abstract).- On tangencies among planar curves]{On tangencies among planar curves with an application to coloring L-shapes.- Semi-random process without replacement.- The intersection spectrum of 3-chromatic intersecting hypergraphs.- On ordered Ramsey numbers of tripartite 3-uniform hypergraphs.- Hypergraphs with minimum positive uniform Turan density.- Rainbow cliques in randomly perturbed dense graphs.- Universal singular exponents in catalytic variable equations.- The expected number of perfect matchings in cubic planar graphs.- Gallai-Ramsey number for complete graphs.- On the dichromatic number of surfaces.- Supersaturation, counting, and randomness inforbidden subposet problems.- Path decompositions of tournaments.- Sorting by shuffling methods and a queue.- Circular coloring of signed bipartite planar graphs.- Results on the Graceful Game and Range-Relaxed Graceful Game.- New bounds on the modularity of Johnson graphs and random subgraphs of Johnson graphs.- On Bipartite Sum Basic Equilibria.- Characterization and enumeration of preimages under the Queuesort algorithm.- On off-diagonal ordered Ramsey numbers of nested matchings.- Bounds on half graph orders in powers of sparse graphs.- The homotopy type of the independence complex of graphs with no induced cycles of length divisible by $3$.- The Maximum Number of Paths of Length Three in a Planar Graph.- Strongly Pfaffian Graphs.- Strong modeling limits of graphs with bounded tree-width.- Loose cores and cycles in random hypergraphs (extended abstract).- Building a larger class of graphs for efficient reconfiguration of vertex colouring.- A refinement of Cauchy-Schwarz complexity, with applications (extended abstract).- The Ising antiferromagnet in the replica symmetric phase.- A simple (2+\epsilon)-approximation algorithm for Split Vertex Deletion.- On graphs without an induced path on 5 vertices and without an induced dart or kite.- Constant congestion brambles in directed graphs.- Component behaviour of random bipartite graphs.- Maximising line subgraphs of diameter at most $t$.- Unavoidable hypergraphs.- $2$-distance $(\Delta+1)$-coloring of sparse graphs using the potential method.- Graphs where Search Methods are Indistinguishable.- Discrete Helly-type theorems for pseudohalfplanes.- Cycles of Many Lengths in Hamiltonian Graphs.- Maximal $k$-wise $\ell$-divisible set families are atomic.- A Trivariate Dichromate Polynomial for Digraphs.- Schur's Theorem for randomly perturbed sets.- Unit Disk Visibility Graphs.- Waiter-Client Games on Randomly Perturbed Graphs.- Vector Choosability in Bipartite Graphs.- Tight bounds on the expected number of holes in random point sets.- The game of Toucher and Isolator.- Hermitian rank-metric codes.- The Flat Wall Theorem for Bipartite Graphs with Perfect Matchings.- Big Ramsey degrees and forbidden cycles.- The Ramsey number for 4-uniform tight cycles.- Chip-firing on the complete split graph: Motzkin words and tiered parking functions.- Long shortest cycle covers in cubic graphs.- Powers of Hamilton cycles of high discrepancy are unavoidable.- Low Diameter Algebraic Graphs.- The fractional chromatic number of double cones over graphs.- Complexity of $3+1/m$-coloring $P_t$-free graphs.- Shattering Threshold for the Coloring Problem of a Random Hypergraph.- Integer covering problems and max-norm Ramsey theorems.- Unit disks hypergraphs are three-colorable.- Characterization of FS-double Squares Ending with Two Distinct Squares.- On asymmetric hypergraphs.- On Multicolour Ramsey Numbers and Subset-Colouring of Hypergraphs.- Max Cuts in Triangle-free Graphs.- On the cycle rank conjecture about metric dimension and zero forcing number in graphs.- Tight bounds for powers of Hamilton cycles in tournaments.- On sufficient conditions for Hamiltonicity in dense graphs.- On the maximum number of weakly-rainbow-free edge-colorings.- Degree conditions for tight Hamilton cycles.- An Approximate Struc...