arXiv subjects

József Pintér

Publications and source records attributed to József Pintér.

9 recordsLinked to original sources

arXiv2026

Meme Template Identification in the Wild: Comparing Methods for Semi-Open-Set Recognition

Image-with-text memes are a dominant form of online communication, and much of their spread happens through meme templates which are recurring visual formats that users adapt with new text or imagery. Most prior work scores memes individually for engagement or harmful content, an approach that is structurally blind to templates. Templates might amplify these patterns and enable coordinated harassment, which becomes visible only when memes are grouped by shared template. We formalize meme template identification as a semi-open-set recognition problem, requiring methods to both classify known templates and reject template-free memes and non-meme content. We introduce an evaluation framework spanning a controlled setting (1,704 ImgFlip templates) and a heterogeneous real-world social media sample, comparing supervised CNN- and distance-based methods, unsupervised density-based clustering, a novel fused SigLIP2+DINOv2 representation, and a retrieval-augmented LLM pipeline. In real-world social media sources dedicated to meme sharing, we find that only 21% of images use a known template, while 58% are template-free and 21% are not memes at all; identification performance also drops sharply from the controlled setting (best MCC 0.974 to 0.684). The loss comes mainly from deciding whether an image is a template-based meme at all, rather than identifying the template. Our dataset of 1.1M soft-labeled social media images, together with code for reproducibility, is available upon request.

cs.CY↗

arXiv2026

Nowhere-zero 4-flows in graphs excluding a proper minor of the Petersen graph

Tutte's $4$-flow conjecture asserts that every finite bridgeless graph with no Petersen minor admits a nowhere-zero $4$-flow. Let $P$ be the Petersen graph and let $e\in E(P)$. We prove that every finite bridgeless $(P/e)$-minor-free multigraph admits a nowhere-zero $4$-flow. Since $P-e$ and $P/e$ are the two maximal proper minors of $P$, combining our result with the theorem of Thomas and Thomson for $(P-e)$-minor-free graphs shows that, for every proper minor $R$ of $P$, every finite bridgeless $R$-minor-free graph admits a nowhere-zero $4$-flow. Equivalently, every finite bridgeless graph without such a flow contains every proper minor of $P$. The proof builds on the girth-five structural framework of Thomas and Thomson together with the nonplanar extension theorem of Norin and Thomas.

math.CO↗

arXiv2026

The crumby coloring conjecture for subcubic outerplanar graphs

The red-blue vertex partitions now known as crumby colorings originate in a conjecture of Thomassen related to Wegner's conjecture on squares of planar graphs. In such a coloring, the blue vertices induce a graph of maximum degree at most one, while the red vertices induce a graph with no isolated vertices and no simple path with three edges. Barát, Blázsik and Damásdi proved that every 2-connected outerplanar graph of maximum degree at most three admits a crumby coloring, and conjectured that the 2-connectivity assumption can be removed. We prove this conjecture: every finite simple subcubic outerplanar graph admits a crumby coloring. To prove the conjecture, we introduce a rooted grammar for subcubic outerplanar graphs. The grammar describes such graphs recursively using rooted branches and two-terminal path fragments; cyclic blocks are handled by deleting the root to obtain a path fragment. We correspondingly extend crumby colorings to crumby-admissible colorings: in a rooted branch the root, and in a path fragment the two terminals, are allowed to be temporary isolated red vertices. This relaxation makes induction along the grammar possible while retaining only finite boundary information. The induction reduces to verifying an explicit finite family of lower certificates, namely nonempty sets of boundary types and root states. The required verification has two parts: the family must be closed under all steps of the decomposition, and every certified completed branch must contain a final-legal root state, so that the temporary defect disappears and the resulting coloring is a genuine crumby coloring. This final step is computer-assisted: a stand-alone certificate checker, supplied with the paper, verifies the stated closure and crumby conditions for the supplied certificate. All structural reductions and the certificate-induction principle are proved by hand.

math.CO↗

arXiv2026

Conformability is NP-complete, even on connected regular graphs

A graph $G$ is conformable if it admits a proper $(Δ(G)+1)$-coloring in which, among the $Δ(G)+1$ color classes including the empty ones, at most $\sum_{v\in V(G)}(Δ(G)-d_G(v))$ have parity different from that of $|V(G)|$. The complexity of deciding conformability was left open in recent work, and positive results for several graph classes had suggested that the problem might be polynomial-time solvable. We settle the general problem by proving that Conformability is NP-complete. Hardness holds even for connected regular graphs $G$ of odd order with independence number $α(G)=3$ and maximum degree $Δ(G)\ge |V(G)|/2$. In particular, NP-completeness persists when every color class is forced to have the parity of the order. The reduction starts from perfect triangle packing in graphs of clique number three, regularizes the source graph while preserving the relevant triangle packings, and then takes the complement. In the complement, conformable color classes correspond to odd cliques of the regularized graph; $K_4$-freeness restricts these cliques to singletons or triangles, and the number of available colors forces exactly the required number of disjoint triangles.

math.CO↗

arXiv2026

Homogeneous Network Caching is Fixed-Parameter Tractable Parameterized by the Number of Caches

Network caching asks how to place contents in distributed caches so that future requests are served close to their users. Ganian, Mc Inerney and Tsigkari recently initiated the parameterized-complexity study of the problem and, for the homogeneous unit-size variant (HomNC), isolated an unresolved family of six parameterizations: by the number of caches $C$, the number of users $U$, $U+K$, $C+U$, $C+λ$, and the vertex-cover number $\text{vc}(G)$, where $K$ is the maximum cache capacity and $λ$ is the maximum number of contents requested with nonzero probability by any user. Their interreducibility theorem showed that these six cases stand or fall together under parameterized reductions, and they conjectured the family to be W[1]-hard. We resolve this conjecture in the opposite direction. We prove that HomNC is fixed-parameter tractable parameterized by $C$ alone, and therefore fixed-parameter tractable for all six parameterizations. Our algorithm is based on an exact $n$-fold integer programming formulation that reveals a nontrivial block structure in homogeneous network caching, with the repeated part depending only on $C$. Standard algorithms for $n$-fold integer programming then yield a running time of the form $f(C)\lvert I\rvert^{O(1)}$.

cs.DS↗

arXiv2026

Subcubic $K_4$-minor-free graphs without crumby colorings

Motivated by Wegner's conjecture on squares of planar graphs, Thomassen conjectured that every 3-connected cubic graph on at least eight vertices admits a red-blue vertex coloring in which the blue subgraph has maximum degree at most 1, while the red subgraph has minimum degree at least 1 and contains no $P_4$. Such colorings are now called crumby colorings. Although this conjecture was disproved in general by Bellitto, Klimošová, Merker, Witkowski and Yuditsky, positive results of Barát, Blázsik and Damásdi led them, in the same subcubic setting, to conjecture that every $K_4$-minor-free graph admits a crumby coloring. We disprove this conjecture with a connected subcubic partial 2-tree on 18 vertices. We also disprove its natural 2-connected version with a 2-connected subcubic partial 2-tree on 40 vertices with no crumby coloring. Consequently, the obstruction to crumby colorability already occurs within treewidth two, even under 2-connectivity.

math.CO↗

arXiv2025

Color-avoiding connected colorings and orientations

We study network robustness under correlated failures modeled by colors, where each color represents a class of edges or vertices that may fail simultaneously. An edge-colored graph is said to be edge-color-avoiding $k$-edge-connected if it remains $k$-edge-connected after the removal of all edges of any single color. We characterize the graphs that admit such a coloring and show that, when $k = 1$, one can determine in polynomial time both the minimum number of colors required and a coloring achieving it; while the problem becomes NP-hard for $k \ge 2$. We also investigate the problem of orienting the edges of a graph so that the resulting digraph remains strongly or rooted connected even after the removal of all arcs of any single color. In addition, we explore generalizations involving vertex-colorings, $k$-vertex-connectivity, simultaneous failures of multiple colors and matroids.

math.CO↗

arXiv2024

Color-avoiding connected spanning subgraphs with minimum number of edges

We call a (not necessarily properly) edge-colored graph edge-color-avoiding connected if after the removal of edges of any single color, the graph remains connected. For vertex-colored graphs, similar definitions of color-avoiding connectivity can be given. In this article, we investigate the problem of determining the maximum number of edges that can be removed from a color-avoiding connected graph so that it remains color-avoiding connected. First, we prove that this problem is NP-hard, then we give a polynomial-time approximation algorithm for it. To analyze the approximation factor of this algorithm, we determine the minimum number of edges of color-avoiding connected graphs on a given number of vertices and with a given number of colors. Furthermore, we also consider a generalization of edge-color-avoiding connectivity to matroids.

math.CO↗

arXiv2023

Tournament schedules and incentives in a double round-robin tournament with four teams

In a round-robin tournament, a team may lack the incentive to win if its final rank does not depend on the outcome of the matches still to be played. This paper introduces a classification scheme to determine these weakly (where one team is indifferent) or strongly (where both teams are indifferent) stakeless matches in a double round-robin contest with four teams. The probability that such matches arise can serve as a novel fairness criterion to compare and evaluate match schedules. Our approach is illustrated by the UEFA Champions League group stage. A simulation model is built to compare the 12 valid schedules for the group matches. Some schedules are shown to be dominated by other schedules. It is found that the strongest team should play at home in the last round against one of the middle teams, depending on the preferences of the tournament organiser. Choosing an optimal sequence of matches with respect to the proposed metric can help to avoid uninteresting matches.

math.OC↗